Chapter 7 Resource Masters - · PDF fileThe Chapter 7 Resource Masters includes the core...
Transcript of Chapter 7 Resource Masters - · PDF fileThe Chapter 7 Resource Masters includes the core...
Chapter 7 Resource Masters
Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters are available as consumable workbooks in both English and Spanish.
ISBN10 ISBN13
Study Guide and Intervention Workbook 0-07-890848-5 978-0-07-890848-4
Homework Practice Workbook 0-07-890849-3 978-0-07-890849-1
Spanish Version
Homework Practice Workbook 0-07-890853-1 978-0-07-890853-8
Answers for Workbooks The answers for Chapter 7 of these workbooks can be found in the back of this Chapter Resource Masters booklet.
StudentWorks PlusTM This CD-ROM includes the entire Student Edition test along with the English workbooks listed above.
TeacherWorks PlusTM All of the materials found in this booklet are included for viewing, printing, and editing in this CD-ROM.
Spanish Assessment Masters (ISBN10: 0-07-890856-6, ISBN13: 978-0-07-890856-9) These masters contain a Spanish version of Chapter 7 Test Form 2A and Form 2C.
Copyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Geometry. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240
ISBN13: 978-0-07-890516 - 2
ISBN10: 0-07-890516-8
Printed in the United States of America
1 2 3 4 5 6 7 8 9 10 009 14 13 12 11 10 09 08
iii
Contents
Teacher’s Guide to Using the Chapter 7
Resource Masters .............................................iv
Chapter ResourcesStudent-Built Glossary ....................................... 1
Anticipation Guide (English) .............................. 3
Anticipation Guide (Spanish) ............................. 4
Lesson 7-1Ratios and Proportions
Study Guide and Intervention ............................ 5
Skills Practice .................................................... 7
Practice .............................................................. 8
Word Problem Practice ..................................... 9
Enrichment ...................................................... 10
Graphing Calculator Activity ............................ 11
Lesson 7-2Similar Polygons
Study Guide and Intervention .......................... 12
Skills Practice .................................................. 14
Practice ............................................................ 15
Word Problem Practice ................................... 16
Enrichment ...................................................... 17
Lesson 7-3Similar Triangles
Study Guide and Intervention .......................... 18
Skills Practice .................................................. 20
Practice ............................................................ 21
Word Problem Practice ................................... 22
Enrichment ...................................................... 23
Lesson 7-4Parallel Lines and Proportional Parts
Study Guide and Intervention .......................... 24
Skills Practice .................................................. 26
Practice ............................................................ 27
Word Problem Practice ................................... 28
Enrichment ...................................................... 29
Lesson 7-5Parts of Similar Triangles
Study Guide and Intervention .......................... 30
Skills Practice .................................................. 32
Practice ............................................................ 33
Word Problem Practice ................................... 34
Enrichment ...................................................... 35
Spreadsheet Activity ........................................ 36
Lesson 7-6Similarity Transformations
Study Guide and Intervention .......................... 37
Skills Practice .................................................. 39
Practice ............................................................ 40
Word Problem Practice ................................... 41
Enrichment ...................................................... 42
Lesson 7-7Scale Drawings and Models
Study Guide and Intervention .......................... 43
Skills Practice .................................................. 45
Practice ............................................................ 46
Word Problem Practice ................................... 47
Enrichment ...................................................... 48
AssessmentStudent Recording Sheet ................................ 49
Rubric for Extended-Response ....................... 50
Chapter 7 Quizzes 1 and 2 ............................. 51
Chapter 7 Quizzes 3 and 4 ............................. 52
Chapter 7 Mid-Chapter Test ............................ 53
Chapter 7 Vocabulary Test ............................. 54
Chapter 7 Test, Form 1 ................................... 55
Chapter 7 Test, Form 2A ................................. 57
Chapter 7 Test, Form 2B ................................. 59
Chapter 7 Test, Form 2C ................................ 61
Chapter 7 Test, Form 2D ................................ 63
Chapter 7 Test, Form 3 ................................... 65
Chapter 7 Extended-Response Test ............... 67
Standardized Test Practice ............................. 68
Answers ........................................... A1–A32
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Teacher’s Guide to Using the
Chapter 7 Resource MastersThe Chapter 7 Resource Masters includes the core materials needed for Chapter 7. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing on the
TeacherWorks PlusTM CD-ROM.
Chapter Resources
Student-Built Glossary (pages 1–2) These masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to recording definitions and/or examples for each term. You may suggest that student highlight or star the terms with which they are not familiar. Give to students before beginning Lesson 7-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.
Anticipation Guide (pages 3–4) This master presented in both English and Spanish is a survey used before beginning the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed.
Lesson Resources
Study Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.
Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the
lesson.
Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for second-day teaching of the lesson.
Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.
Enrichment These activities may extend the concepts of the lesson, offer a historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. They are written for use with all levels of students.
Graphing Calculator, TI-Nspire, or
Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.
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Assessment OptionsThe assessment masters in the Chapter 7
Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.
Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.
Extended-Response Rubric This master provides information for teachers and students on how to assess performance on open-ended questions.
Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.
Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 10 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.
Leveled Chapter Tests
• Form 1 contains multiple-choice questions and is intended for use with below grade level students.
• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Form 3 is a free-response test for use with above grade level students.
All of the above mentioned tests include a free-response Bonus question.
Extended-Response Test Performance assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation.
Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided as reduced pages.
• Full-size answer keys are provided for the assessment masters.
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This is an alphabetical list of the key vocabulary terms you will learn in Chapter 7.
As you study the chapter, complete each term’s definition or description.
Remember to add the page number where you found the term. Add these pages to
your Geometry Study Notebook to review vocabulary at the end of the chapter.
(continued on the next page)
Chapter 7 1 Glencoe Geometry
Student-Built Glossary
Vocabulary TermFound
on PageDe! nition/Description/Example
cross products
dilation
enlargement
means
midsegment of a triangle
proportion
7
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Chapter 7 2 Glencoe Geometry
Vocabulary TermFound
on PageDe! nition/Description/Example
ratio
reduction
scale drawing
scale factor
scale model
similar polygons
similarity transformation
Student-Built Glossary (continued)7
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Chapter 7 3 Glencoe Geometry
Anticipation Guide
Proportions and Similarity
7
Before you begin Chapter 7
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
After you complete Chapter 7
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
Step 2
Step 1
STEP 1A, D, or NS
StatementSTEP 2A or D
1. Ratios are always written as fractions.
2. A proportion is an equation stating that two ratios are equal.
3. Two ratios are in proportion to each other only if their cross products are equal.
4. If a −
b =
c −
d , then ad = bc.
5. The ratio of the lengths of the sides of similar figures is called the scale factor for the two figures.
6. If one angle in a triangle is congruent to an angle in another triangle, then the two triangles are similar.
7. If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then the line separates the two sides into congruent segments.
8. A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle.
9. If two triangles are similar then their perimeters are equal.
10. The medians of two similar triangles are in the same proportion as corresponding sides.
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NOMBRE FECHA PERÍODO
Antes de comenzar el Capítulo 7
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a).
Después de completar el Capítulo 7
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.
Ejercicios preparatorios
Proporciones y Semejanzas
Paso 1
PASO 1A, D o NS
EnunciadoPASO 2A o D
1. Las razones se escriben siempre como fracciones.
2. Una proporción es una ecuación que establece que dos razones son iguales.
3. Dos razones son proporcionales entre sí sólo si sus productos cruzados son iguales.
4. Si a −
b =
c −
d , entonces ad = bc.
5. La razón de las longitudes de los lados de figuras semejantes se llama factor de escala para las dos figuras.
6. Si un ángulo de un triángulo es congruente a un ángulo de otro triángulo, entonces los dos triángulos son semejantes.
7. Si una recta es paralela a un lado del triángulo e interseca los otros dos lados en dos puntos diferentes, entonces la recta separa los dos lados en segmentos congruentes.
8. Un segmento cuyos extremos son los puntos medios de dos lados de un triángulo es paralelo al tercer lado del triángulo.
9. Si dos triángulos son semejantes, éstos tienen el mismo perímetro.
10. Las medianas de dos triángulos semejantes están en la misma proporción que los lados correspondientes.
Paso 2
7
Capítulo 7 4 Geometría de Glencoe
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Lesso
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-1
Chapter 7 5 Glencoe Geometry
Study Guide and Intervention
Ratios and Proportions
Write and Use Ratios A ratio is a comparison of two quantities by divisions. The ratio a to b, where b is not zero, can be written as
a −
b or a:b.
In 2007 the Boston RedSox baseball team won 96 games out of 162
games played. Write a ratio for the number of games won to the total number of
games played.
To find the ratio, divide the number of games won by the total number of games played. The
result is 96 −
162 , which is about 0.59. The Boston RedSox won about 59% of their games in
2007.
The ratio of the measures of the angles
in △JHK is 2:3:4. Find the measures of the angles.
The extended ratio 2:3:4 can be rewritten 2x:3x:4x.
Sketch and label the angle measures of the triangle. Then write and solve an equation to find the value of x.
2x + 3x + 4x = 180 Triangle Sum Theorem
9x = 180 Combine like terms.
x = 20 Divide each side by 9.
The measures of the angles are 2(20) or 40, 3(20) or 60, and 4(20) or 80.
Exercises
1. In the 2007 Major League Baseball season, Alex Rodriguez hit 54 home runs and was at bat 583 times. What is the ratio of home runs to the number of times he was at bat?
2. There are 182 girls in the sophomore class of 305 students. What is the ratio of girls to total students?
3. The length of a rectangle is 8 inches and its width is 5 inches. What is the ratio of length to width?
4. The ratio of the sides of a triangle is 8:15:17. Its perimeter is 480 inches. Find the length of
each side of the triangle.
5. The ratio of the measures of the three angles of a triangle is 7:9:20. Find the measure of each
angle of the triangle.
Example 1
Example 2
7-1
4x° 2x°
3x°
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Chapter 7 6 Glencoe Geometry
Study Guide and Intervention (continued)
Ratios and Proportions
Use Properties of Proportions A statement that two ratios are
equal is called a proportion. In the proportion a − b = c −
d , where b and d are
not zero, the values a and d are the extremes and the values b and c
are the means. In a proportion, the product of the means is equal to the
product of the extremes, so ad = bc. This is the Cross Product Property.
Solve 9 −
16 =
27 −
x .
9 − 16
= 27 −
x
9 · x = 16 · 27 Cross Products Property
9x = 432 Multiply.
x = 48 Divide each side by 9.
POLITICS Mayor Hernandez conducted a random survey of
200 voters and found that 135 approve of the job she is doing. If there are
48,000 voters in Mayor Hernandez’s town, predict the total number of voters
who approve of the job she is doing.
Write and solve a proportion that compares the number of registered voters and the number of registered voters who approve of the job the mayor is doing.
135 −
200 = x
− 48,000
← voters who approve
← all voters
135 · 48,000 = 200 · x Cross Products Property
6,480,000 = 200x Simplify.
32,400 = x Divide each side by 200.
Based on the survey, about 32,400 registered voters approve of the job the mayor is doing.
Exercises
Solve each proportion.
1. 1 − 2 = 28
− x 2.
3 −
8 =
y −
24 3.
x + 22 −
x + 2 = 30
− 10
4. 3 −
18.2 = 9 − y 5.
2x + 3 −
8 = 5 −
4 6.
x + 1 −
x - 1 = 3 −
4
7. If 3 DVDs cost $44.85, find the cost of one DVD.
8. BOTANY Bryon is measuring plants in a field for a science project. Of the first 25 plants he measures, 15 of them are smaller than a foot in height. If there are 4000 plants in the field, predict the total number of plants smaller than a foot in height.
7-1
Example 1
Example 2
a − b = c −
d
a · d = b · c
extremes means↑ ↑
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Lesso
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-1
Chapter 7 7 Glencoe Geometry
Skills Practice
Ratios and Proportions
7-1
1. FOOTBALL A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdowns
per game.
2. EDUCATION In a schedule of 6 classes, Marta has 2 elective classes. What is the ratio
of elective to non-elective classes in Marta’s schedule?
3. BIOLOGY Out of 274 listed species of birds in the United States, 78 species made the
endangered list. Find the ratio of endangered species of birds to listed species in the
United States.
4. BOARD GAMES Myra is playing a board game. After 12 turns, Myra has landed on a
blue space 3 times. If the game will last for 100 turns, predict how many times Myra
will land on a blue space.
5. SCHOOL The ratio of male students to female students in the drama club at Campbell
High School is 3:4. If the number of male students in the club is 18, predict the number
of female students?
Solve each proportion.
6. 2 − 5 =
x −
40 7.
7 −
10 = 21
− x 8.
20 −
5 =
4x −
6
9. 5x
− 4 =
35 −
8 10.
x+1 −
3 =
7 −
2 11.
15 −
3 =
x-3 −
5
12. The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is
450 centimeters. Find the measures of each side of the triangle.
13. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 220 meters.
What are the measures of the sides of the triangle?
14. The ratio of the measures of the sides of a triangle is 4:6:8, and its perimeter is 126 feet.
What are the measures of the sides of the triangle?
15. The ratio of the measures of the sides of a triangle is 5:7:8, and its perimeter is 40 inches.
Find the measures of each side of the triangle.
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Chapter 7 8 Glencoe Geometry
Practice
Ratios and Proportions
1. NUTRITION One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fat
are saturated fats. Find the ratio of saturated fats to total fat in an ounce of cheese.
2. FARMING The ratio of goats to sheep at a university research farm is 4:7. The number
of sheep at the farm is 28. What is the number of goats?
3. QUALITY CONTROL A worker at an automobile assembly plant checks new cars for
defects. Of the first 280 cars he checks, 4 have defects. If 10,500 cars will be checked this
month, predict the total number of cars that will have defects.
Solve each proportion.
4. 5 −
8 =
x −
12 5.
x −
1.12 = 1 −
5 6.
6x −
27 = 43
7. x + 2
− 3 =
8 −
9 8.
3x - 5 −
4 =
-5 −
7 9. x -2
− 4 =
x + 4 −
2
10. The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet.
Find the measure of each side of the triangle.
11. The ratio of the measures of the sides of a triangle is 7:9:12, and its perimeter is
84 inches. Find the measure of each side of the triangle.
12. The ratio of the measures of the sides of a triangle is 6:7:9, and its perimeter is
77 centimeters. Find the measure of each side of the triangle.
13. The ratio of the measures of the three angles is 4:5:6. Find the measure of each angle of
the triangle.
14. The ratio of the measures of the three angles is 5:7:8. Find the measure of each angle of
the triangle.
15. BRIDGES A construction worker is placing rivets in a new bridge. He uses 42 rivets to build
the first 2 feet of the bridge. If the bridge is to be 2200 feet in length, predict the number of
rivets that will be needed for the entire bridge.
7-1
Lesso
n 7
-1
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Chapter 7 9 Glencoe Geometry
Word Problem Practice
Ratios and Proportions
1. TRIANGLES The ratios of the measures
of the angles in △DEF is 7:13:16.
13x°
16x°
7x°
Find the measure of the angles.
2. RATIONS Sixteen students went on
a week-long hiking trip. They brought
with them 320 specially baked, protein-
rich, cookies. What is the ratio of cookies
to students?
3. CLOVERS Nathaniel is searching for
a four-leaf clover in a field. He finds
2 four-leaf clovers during the first
12 minutes of his search. If Nathaniel
spends a total of 180 minutes searching
in the field, predict the number of four-
leaf clovers Nathaniel will find.
4. CARS A car company builds two
versions of one of its models—a sedan
and a station wagon. The ratio of sedans
to station wagons is 11:2. A freighter
begins unloading the cars at a dock.
Tom counts 18 station wagons and then
overhears a dock worker call out, “Okay,
that’s all of the wagons . . . bring out
the sedans!” How many sedans were on
the ship?
5. DISASTER READINESS The town of
Oyster Bay is conducting a survey of
80 households to see how prepared its
citizens are for a natural disaster. Of
those households surveyed, 66 have a
survival kit at home.
a. Write the ratio of people with
survival kits in the survey.
b. Write the ratio of people without
survival kits in the survey.
c. There are 29,000 households in
Oyster Bay. If the town wishes to
purchase survival kits for all
households that do not currently have
one, predict the number of kits it will
have to purchase.
7-1
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Chapter 7 10 Glencoe Geometry
Enrichment
Growth Charts
It is said that when a child has reached the age of 2 years, he is roughly half of his adult
height. The growth chart below shows the growth according to percentiles for boys.
1. Use the chart to determine the approximate height for a boy at age 2 if he is in the 75th
to 95th percentile.
2. Using the rule that the height at age 2 is approximately half of his adult height, set up a
proportion to solve for the adult height of the boy in Exercise 1. Solve your proportion.
3. Use the chart to approximate the height at age 18 for a boy if he is in the 75th to 95th
percentile. How does this answer compare to the answer to problem 1?
4. Repeat this process for a boy who is in the 5th to 25th percentile.
5. Is using the rule that a boy is half of his adult height at age 2 years a good
approximation? Explain.
7-1
85
75
65
55
45
35
2 4 6 8 10 12 14 16 18
Age (yr)
Heig
ht
(in
.)
Percentile Group
5th to 25th
25th to 75th
75th to 95th
A
B
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Lesso
n 7
-1
Chapter 7 11 Glencoe Geometry
You can use a calculator to solve proportions.
Solve the proportion by using cross products. Round your answer
to the nearest hundredth.
55.6
− 16.9
= 45.8
− x
Multiply 16.9 by 45.8. Divide the product by 55.6.
Enter: 16.9 3 45.8 ÷ 55.6 ENTER 13.92122302
The solution is approximately 13.92
Solve each proportion by using cross products. Round your answers
to the nearest hundredth.
1. 13.9
− 39.8
= 10.5
− x 2.
25.9 −
37.7 =
24.3 −
x 3.
19.6 −
54.3 =
27.7 −
x
4. 66.8
− 43.4
= x −
16.9 5.
75.4 −
37.2 =
x −
32.4 6.
x −
46.2 =
29.7 −
36.4
7. x −
14.9 =
16.8 −
24.6 8.
35.8 −
x =
32.9 −
27.8 9.
46.9 −
x =
15.7 −
99.9
10. 34.9
− 21.1
= x −
36.6 11.
x −
99.8 =
32.2 −
45.3 12.
68.9 −
x =
44.3 −
86.4
7-1 Graphing Calculator Activity
Solving Proportions
Example
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Chapter 7 12 Glencoe Geometry
Identify Similar Polygons Similar polygons have the same shape but not necessarily the same size.
If △ABC ∼ △XYZ, list all pairs of congruent angles and
write a proportion that relates the corresponding sides.
Use the similarity statement.
Congruent angles: ∠A ! ∠X, ∠B ! ∠Y, ∠C ! ∠Z
Proportion: AB −
XY =
BC −
YZ =
CA −
ZX
Determine whether the pair of figures is similar. If so, write the
similarity statement and scale factor. Explain your reasoning.
Step 1 Compare corresponding angles.
∠W ! ∠P, ∠X ! ∠Q, ∠Y ! ∠R, ∠Z ! ∠S
Corresponding angles are congruent.
Step 2 Compare corresponding sides.
WX
− PQ
= 12
− 8 =
3 −
2 , XY
− QR
= 18
− 12
= 3 −
2 , YZ
− RS
= 15
− 10
= 3 −
2 , and
ZW
− SP
= 9 −
6 =
3 −
2 . Since corresponding sides are proportional,
WXYZ ∼ PQRS. The polygons are similar with a scale factor of 3 −
2 .
Exercises
List all pairs of congruent angles, and write a
proportion that relates the corresponding sides
for each pair of similar polygons.
1. △DEF ∼ △GHJ
2. PQRS ∼ TUWX
Determine whether each pair of figures is similar. If so, write the similarity
statement and scale factor. If not, explain your reasoning.
3. 4.
22
11
7-2 Study Guide and Intervention
Similar Polygons
Example 1
15
9
12
18
XW
ZY
10
6
8
12
QP
S R
Example 2
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Chapter 7 13 Glencoe Geometry
Study Guide and Intervention (continued)
Similar Polygons
Use Similar Figures You can use scale factors and proportions to find missing side lengths in similar polygons.
The two polygons are
similar. Find x and y.
x
y38
32
16 13
T
S
R P
N
M
Use the congruent angles to write the corresponding vertices in order.
△RST ∼ △MNP
Write proportions to find x and y.
32
− 16
= x −
13
38 − y =
32 −
16
16x = 32(13) 32y = 38(16)
x = 26 y = 19
If △DEF ∼ △GHJ, find the
scale factor of △DEF to △GHJ and the
perimeter of each triangle.
The scale factor is
EF −
HJ =
8 −
12 = 2 −
3 .
The perimeter of △DEF is 10 + 8 + 12 or 30.
2 − 3 =
Perimeter of △DEF −−
Perimeter of △GHJ Theorem 7.1
2 − 3 =
30 − x Substitution
(3)(30) = 2x Cross Products Property
45 = x Solve.
So, the perimeter of △GHJ is 45.
Exercises
Each pair of polygons is similar. Find the value of x.
1.
9
12
8
10x
2.
10
4.5x
2.5
5
3. 12
x + 1
18
24
18
4.
40
36x +15
30
18
5. If ABCD ∼ PQRS, find the scale factor
of ABCD to PQRS and the perimeter
of each polygon.
7-2
Example 1 Example 2
12
12
10
8
14
20
25
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Chapter 7 14 Glencoe Geometry
Determine whether each pair of figures is similar. If so, write the similarity
statement and scale factor. If not, explain your reasoning.
1. 2.
7.5
7.5
7.5
7.5
Z Y
XW
3
3
33
S R
QP
Each pair of polygons is similar. Find the value of x.
3. 4.
5. 6.
9
10
3
x + 1
5
P
S
R
U V
WT
Q
10
8
x + 2
x - 1
SP
M N
L
T
x + 5
x + 5
9
3
44S
W
XY
T
U26
14
12 13
B C
DA
13
7
6 x
G
E H
F
10.5
6 9
59° 35°A C
B
7
4 6
59° 35°D F
E
Skills Practice
Similar Polygons
7-2
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Chapter 7 15 Glencoe Geometry
Practice
Similar PolygonsDetermine whether each pair of figures is similar. If so, write the similarity
statement and scale factor. If not, explain your reasoning.
1.
25 12
9
14.4
15
2420
15
JM Q R
S
PKL
2.
2412
14 162118
VUAC
BT
Each pair of polygons is similar. Find the value of x.
3.
14
10
x + 6
x + 9
C N MD
A BLP
4.
6 12
40°
40°
x + 1
x - 3A
F
E
D
B C
5. PENTAGONS If ABCDE ∼ PQRST, find the
scale factor of ABCDE to PQRST and the
perimeter of each polygon.
6. SWIMMING POOLS The Minnitte family
and the neighboring Gaudet family both
have in-ground swimming pools. The
Minnitte family pool, PQRS, measures
48 feet by 84 feet. The Gaudet family pool,
WXYZ, measures 40 feet by 70 feet. Are
the two pools similar? If so, write the
similarity statement and scale factor.
7-2
2015
10
21
48 ft
84 ft
70 ft
40 ftP
Q
S W
Z
X
Y
R
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Chapter 7 16 Glencoe Geometry
Word Problem Practice
Similar Polygons
1. PANELS When closed, an entertainment
center is made of four square panels.
The three smaller panels are congruent
squares.
What is the scale factor of the larger
square to one of the smaller squares?
2. WIDESCREEN TELEVISIONS An
electronics company manufactures
widescreen television sets in several
different sizes. The rectangular viewing
area of each television size is similar to
the viewing areas of the other sizes. The
company’s 42-inch widescreen television
has a viewing area perimeter of
approximately 144.4 inches. What is the
viewing area perimeter of the company’s
46-inch widescreen television?
3. ICE HOCKEY An official Olympic-sized
ice hockey rink measures 30 meters by
60 meters. The ice hockey rink at the
local community college measures 25.5
meters by 51 meters. Are the ice hockey
rinks similar? Explain your reasoning.
4. ENLARGING Camille wants to make
a pattern for a four-pointed star with
dimensions twice as long as the one
shown. Help her by drawing a star
with dimensions twice as long on the
grid below.
5. BIOLOGY A paramecium is a small
single-cell organism. The paramecium
magnified below is actually one tenth
of a millimeter long.
a. If you want to make a photograph of
the original paramecium so that its
image is 1 centimeter long, by what
scale factor should you magnify it?
b. If you want to make a photograph of
the original paramecium so that its
image is 15 centimeters long, by what
scale factor should you magnify it?
c. By approximately what scale factor
has the paramecium been enlarged
to make the image shown?
7-2
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Chapter 7 17 Glencoe Geometry
Enrichment
Constructing Similar PolygonsHere are four steps for constructing a polygon that is similar to and with sides twice as long as those of an existing polygon.
Step 1 Choose any point either inside or outside the polygon and label it O.
Step 2 Draw rays from O through each vertex of the polygon.
Step 3 For vertex V, set the compass to length OV. Then locate a new point V′ on ray OV such that VV′ = OV. Thus, OV′ = 2(OV).
Step 4 Repeat Step 3 for each vertex. Connect points V′, W′, X′ and Y′ to form the new polygon.
Two constructions of polygons similar to and with sides twice those of VWXY are shown below. Notice that the placement of point O does not affect the size or shape of V′W′X′Y′, only its location.
VW
Y X
VW
Y X
V'
W'
X'Y'
O
VW
YX
V'
W'
X'Y'
O
Trace each polygon. Then construct a similar polygon with sides twice as long as
those of the given polygon.
1.
C
A
B
2. DE
F
G
3. Explain how to construct a similar polygon with sides three times the length of those of polygon HIJKL. Then do the construction.
4. Explain how to construct a similar
polygon 1 1 − 2 times the length of those of
polygon MNPQRS. Then do the construction.
7-2
M
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Chapter 7 18 Glencoe Geometry
Study Guide and Intervention
Similar Triangles
Identify Similar Triangles Here are three ways to show that two triangles are similar.
AA Similarity Two angles of one triangle are congruent to two angles of another triangle.
SSS Similarity The measures of the corresponding side lengths of two triangles are proportional.
SAS SimilarityThe measures of two side lengths of one triangle are proportional to the measures of two
corresponding side lengths of another triangle, and the included angles are congruent.
Determine whether the
triangles are similar.
15
129
D E
F
10
86
A B
C
AC −
DF =
6 −
9 = 2 −
3
BC −
EF =
8 −
12 = 2 −
3
AB −
DE =
10 −
15 = 2 −
3
△ABC ∼ △DEF by SSS Similarity.
Determine whether the
triangles are similar.
8
4
70°
Q
R S6
3
70°
M
N P
3 −
4 =
6 −
8 , so
MN −
QR =
NP −
RS .
m∠N = m∠R, so ∠N & ∠R.
△NMP ∼ △RQS by SAS Similarity.
Exercises
Determine whether the triangles are similar. If so, write a similarity statement.
Explain your reasoning.
1.
A
B
C
D
E
F
2.
36
2018
24
J
K
L
W X
Y
3. RS
UL
T
4.
18
8
65°9
465°
D
K J
P
ZR
5.
39
26
1624
F
B E
L
MN
6. 32
20
154025
24
G H
Q R
SI
7-3
Example 1 Example 2
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Chapter 7 19 Glencoe Geometry
Study Guide and Intervention (continued)
Similar Triangles
Use Similar Triangles Similar triangles can be used to find measurements.
△ABC ∼ △DEF. Find the
values of x and y.
18√3
B
CA
18 189
y
x
E
FD
AC
− DF
= BC
− EF
AB −
DE =
BC −
EF
18 √ $ 3
− x =
18 −
9
y −
18 =
18 −
9
18x = 9(18 √ $ 3 ) 9y = 324
x = 9 √ $ 3 y = 36
A person 6 feet tall casts
a 1.5-foot-long shadow at the same time
that a flagpole casts a 7-foot-long
shadow. How tall is the flagpole?
7 ft
6 ft
?
1.5 ft
The sun’s rays form similar triangles.
Using x for the height of the pole, 6 −
x =
1.5 −
7 ,
so 1.5x = 42 and x = 28.
The flagpole is 28 feet tall.
Exercises
ALGEBRA Identify the similar triangles. Then find each measure.
1. JL 2. IU
3. QR 4. BC
5. LM 6. QP
7. The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter post casts a shadow that is 0.85 meter long, what is the length of the longer post’s shadow to the nearest hundredth?
x32
10
2230
PQ
N
R
F
x
9
8
7.2
16
K
VP M
L
24
36√2x
3636
Q V
R
S
T
35
13
10 20
J L
K
Y
X Zx
x
60
38.6
23
30
E
BA
C D
20
13
26
I
UW
G
H
x
7-3
Example 1 Example 2
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Chapter 7 20 Glencoe Geometry
Determine whether each pair of triangles is similar. If so, write a similarity
statement. If not, what would be sufficient to prove the triangles similar? Explain
your reasoning.
1. 2.
3. 4.
21
70°
15
MJ
P
1470°10
U
S
T
30°60°RQ
M
S
K
T
ALGEBRA Identify the similar triangles. Then find each measure.
5. AC 6. JL
15
12
D
E CB
Ax + 1
x + 5
16
4
M
NL
J
K
x + 18
x - 3
7. EH 8. VT
12
9
6
9
D
E
FH
Gx + 5
6
14
S
U
V
R T
3x - 3
x + 2
12
128
9
96
C P
QR
A
B
Skills Practice
Similar Triangles
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Chapter 7 21 Glencoe Geometry
Practice
Similar Triangles
Determine whether the triangles are similar. If so, write a similarity statement. If
not, what would be sufficient to prove the triangles similar? Explain your
reasoning.
1. 2.
ALGEBRA Identify the similar triangles. Then find each measure.
3. LM, QP 4. NL, ML
5. 6.
8
N
J LK
Mx + 5
6x + 2
24
12
18
N
P
QL
M
x + 3
x - 1
42°
42°
24
1812
16J
A K
Y S
W
7-3
105
12
8
86
x + 7x - 1
x + 1
x + 33
4
7. INDIRECT MEASUREMENT A lighthouse casts a 128-foot shadow. A nearby lamppost
that measures 5 feet 3 inches casts an 8-foot shadow.
a. Write a proportion that can be used to determine the height of the lighthouse.
b. What is the height of the lighthouse?
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Chapter 7 22 Glencoe Geometry
Word Problem Practice
Similar Triangles
A
B
D
E
C
1. CHAIRS A local furniture store sells two
versions of the same chair: one for
adults, and one for children. Find the
value of x such that the chairs are
similar.
18˝
16˝
X
12˝
2. BOATING The two sailboats shown are
participating in a regatta. Find the
value of x.
168.5 in. 220 in.
X in. 264 in.
40°40°
3. GEOMETRY Georgia draws a regular
pentagon and starts connecting its
vertices to make a
5-pointed star. After
drawing three of the
lines in the star, she
becomes curious
about two triangles
that appear in the
figure, △ABC and
△CEB. They look similar to her. Prove
that this is the case.
4. SHADOWS A radio tower casts a
shadow 8 feet long at the same time
that a vertical yardstick casts a shadow
half an inch long. How tall is the radio
tower?
5. MOUNTAIN PEAKS Gavin and Brianna
want to know how far a mountain peak
is from their houses. They measure the
angles between the line of site to the
peak and to each other’s houses and
carefully make the drawing shown.
Gavin
Brianna
Peak
2 in.
2.015 in.
0.246 in.90˚
83˚
The actual distance between Gavin and
Brianna’s houses is 1 1−2
miles.
a. What is the actual distance of the
mountain peak from Gavin’s house?
Round your answer to the nearest
tenth of a mile.
b. What is the actual distance of the
mountain peak from Brianna’s house?
Round your answer to the nearest
tenth of a mile.
7-3
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Chapter 7 23 Glencoe Geometry
Moving Shadows
Have you ever watched your shadow as you
walked along the street at night and observed
how its shape changes as you move? Suppose
a man who is 6 feet tall is standing below
a lamppost that is 20 feet tall. The man is
walking away from the lamppost at a rate of
5 feet per second.
1. If the man is moving at a rate of 5 feet per
second, make a conjecture as to the rate
that his shadow is moving.
2. How far away from the lamppost is the man after 8 seconds?
3. How far is the end of his shadow from the bottom of the lamppost after
8 seconds? Use similar triangles to solve this problem.
4. After 3 more seconds, how far from the lamppost is the man? How far from the lamppost
is his shadow?
5. How many feet did the man move in 3 seconds? How many feet did the shadow move in
3 seconds?
6. The man is moving at a rate of 5 feet/second. What rate is his shadow moving? How
does this rate compare to the conjecture you made in Exercise 1? Make a conjecture as to
why the results are like this.
20 ft
6 ft
x ft
5 ft/sec
Enrichment7-3
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Chapter 7 24 Glencoe Geometry
Study Guide and Intervention
Parallel Lines and Proportional Parts
Proportional Parts within Triangles In any triangle, a line parallel to one side of a triangle separates the other two sides proportionally. This is the Triangle Proportionality Theorem.The converse is also true.
If "# XY ‖ "# RS , then RX
− XT
= SY
− YT
. If RX
− XT
= SY
− YT
, then "# XY ‖ "# RS .
If X and Y are the midpoints of −− RT and
−− ST , then −− XY is a
midsegment of the triangle. The Triangle Midsegment Theorem
states that a midsegment is parallel to the third side and is half its length.
If −− XY is a midsegment, then "# XY ‖ "# RS and XY = 1 −
2 RS.
YS
T
R
X
In △ABC, −−
EF ‖ −−
CB . Find x.
F
C
BA
18
x + 22 x + 2
6E
Since −− EF ‖
−−− CB , AF −
FB = AE
− EC
.
x + 22
− x + 2
= 18
− 6
6x + 132 = 18x + 36
96 = 12x
8 = x
In △GHJ, HK = 5,
KG = 10, and JL is one-half the length
of −−
LG . Is −−−
HK ‖ −− KL ?
Using the converse of the Triangle
Proportionality Theorem, show that
HK −
KG =
JL −
LG .
Let JL = x and LG = 2 x.
HK −
KG = 5 −
10 = 1 −
2
JL −
LG = x −
2x = 1 −
2
Since 1 − 2 = 1 −
2 , the sides are proportional and
−−− HJ ‖ −− KL .
Exercises
ALGEBRA Find the value of x.
1. 5
5 x
7 2.
9
20
x
18 3.
35
x
4.
30 10
24
x 5. 11
x + 12
x
33
6.
30 10
x + 10
x
7-4
Example 1 Example 2
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Chapter 7 25 Glencoe Geometry
Study Guide and Intervention (continued)
Parallel Lines and Proportional Parts
Proportional Parts with Parallel Lines When three or more parallel lines cut two transversals, they separate the transversals into proportional parts. If the ratio of the parts is 1, then the parallel lines separate the transversals into congruent parts.
If ℓ1 ‖ ℓ
2 ‖ ℓ
3, If ℓ
4 ‖ ℓ
5 ‖ ℓ
6 and
then a −
b =
c −
d .
u − v = 1, then
w − x = 1.
Refer to lines ℓ1, ℓ
2, and ℓ
3 above. If a = 3, b = 8, and c = 5, find d.
ℓ1 ‖ ℓ
2 ‖ ℓ
3 so
3 −
8 =
5 −
d . Then 3d = 40 and d = 13 1 −
3 .
Exercises
ALGEBRA Find x and y.
1.
x + 12 12
3x5x
2. 2x - 6
x + 3
12
3.
2x + 4
3x - 1 2y + 2
3y
4.
5
8 y + 2
y
5. 3 4
x + 4x
6.
1632
y + 3y
a
bd
u v
xw
ct
n
m
s ℓ1
ℓ4 ℓ5 ℓ6
ℓ2
ℓ3
7-4
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Chapter 7 26 Glencoe Geometry
1. If JK = 7, KH = 21, and JL = 6, 2. If RU = 8, US = 14, TV = x - 1,
find LI. and VS = 17.5, find x and TV.
Determine whether −−
BC ‖ −−
DE . Justify your answer.
3. AD = 15, DB = 12, AE = 10, and EC = 8
4. BD = 9, BA = 27, and CE = 1 −
3 EA
5. AE = 30, AC = 45, and AD = 2DB
−−
JH is a midsegment of △KLM. Find the value of x.
6.
30
x
7.
9
x
8.
8
x
ALGEBRA Find x and y.
9.
2x + 1 3y - 8
y + 5x + 7
10.
3–2x + 2
x + 3
2y - 1
3y - 5
C
B
E
D
A
R
U V
T
S
HL
K J
I
Skills Practice
Parallel Lines and Proportional Parts
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Chapter 7 27 Glencoe Geometry
Practice
Parallel Lines and Proportional Parts
1. If AD = 24, DB = 27, and EB = 18, 2. If QT = x + 6, SR = 12, PS = 27, and
find CE. TR = x - 4, find QT and TR.
Determine whether −−
JK ‖ −−−
NM . Justify your answer.
3. JN = 18, JL = 30, KM = 21, and ML = 35
4. KM = 24, KL = 44, and NL = 5 −
6 JN
−−
JH is a midsegment of △KLM. Find the value of x.
5.
22x
6.
x + 7
x
7. Find x and y. 8. Find x and y.
3x - 42–3y + 3
1–3y + 65
–4x + 3
4–3y + 2
3x - 4 x + 1
4y - 4
9. MAPS On a map, Wilmington Street, Beech Drive, and Ash Grove
Lane appear to all be parallel. The distance from Wilmington to
Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet.
If the distance between Beech and Ash Grove along Magnolia is
280 feet, what is the distance between the two streets along
Kendall?
Ash Grove
Beech
Magnolia Kendall
Wilmington
NLJ
KM
S
Q
T
RP
D
E
C
BA
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Chapter 7 28 Glencoe Geometry
Word Problem Practice
Parallel Lines and Proportional Parts
Meeeeowww!
30 ft
40 ft
46 ft
x
8 ft 8 ft
10 ft
24 ft
10 ft
x
Cay St.
1 km 1.4 km
0.8 km
Bay St.
Dal
e S
t.
Earl St.
(not drawn to scale)
x
1. CARPENTRY Jake is
fixing an A-frame.
He wants to add a
horizontal support
beam halfway up
and parallel to
the ground. How
long should this
beam be?
2. STREETS In the diagram, Cay Street
and Bay Street are parallel. Find x.
3. JUNGLE GYMS Prassad is building a
two-story jungle gym according to the
plans shown. Find x.
4. FIREMEN A cat
is stuck in a tree
and firemen try to
rescue it. Based
on the figure, if a
fireman climbs
to the top of the
ladder, how far
away is the cat?
5. EQUAL PARTS Nick has a stick that he
would like to divide into 9 equal parts.
He places it on a piece of grid paper as
shown. The grid paper is ruled so that
vertical and horizontal lines are equally
spaced.
a. Explain how he can use the grid
paper to help him find where he
needs to cut the stick.
b. Suppose Nick wants to divide his
stick into 5 equal parts utilizing the
grid paper. What can he do?
8 feet
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Chapter 7 29 Glencoe Geometry
Enrichment
Parallel Lines and Congruent Parts
There is a theorem stating that if three parallel lines cut off congruent segments on one
transversal, then they cut off congruent segments on any transversal. This can be shown
for any number of parallel lines. The following drafting technique uses this fact to divide a
segment into congruent parts.
−− AB to be separated into five congruent parts. This can be
done very accurately without using a ruler. All that is needed
is a compass and a piece of notebook paper.
Step 1 Hold the corner of a piece of notebook paper at
point A.
Step 2 From point A, draw a segment along the paper
that is five spaces long. Mark where the lines
of the notebook paper meet the segment. Label
the fifth point P.
Step 3 Draw −−
PB . Through each of the other marks
on −−
AP , construct a line parallel to −−
BP . The
points where these lines intersect −−
AB will
divide −−
AB into five congruent segments.
Use a compass and a piece of notebook paper to divide
each segment into the given number of congruent parts.
1. six congruent parts
2. seven congruent parts A B
A B
A
P
B
A B
P
A B
A B
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Chapter 7 30 Glencoe Geometry
7-5 Study Guide and Intervention
Parts of Similar Triangles
Special Segments of Similar Triangles When two triangles are similar, corresponding altitudes, angle bisectors, and medians are proportional to the corresponding sides.
Exercises
Find x.
1. x
36
1820
2.
69
12x
3.
3
3
4
x
4.
10
10x
8
87
5.
45
42
x
30 6.
14
12
12
x
Example In the figure, △ABC ∼ △XYZ, with angle bisectors as shown. Find x.
Since △ABC ∼ △XYZ, the measures of the angle bisectors are proportional to the measures of a pair of corresponding sides.
AB −
XY = BD
− WY
24 −
x =
10 −
8
10x = 24(8)
10x = 192
x = 19.2
24
10
DW
Y
ZXC
B
A
8
x
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Less
on
7-5
Chapter 7 31 Glencoe Geometry
7-5 Study Guide and Intervention (continued)
Parts of Similar Triangles
Triangle Angle Bisector Theorem An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides.
Find x.
Since −−−
SU is an angle bisector, RU
− TU
= RS
− TS
.
x −
20 =
15 −
30
30x = 20(15)
30x = 300
x = 10
Exercises
Find the value of each variable.
1. 25
20 28
x 2.
15 9
3a
3.
36 42
46.8
n
4.
10
15
13x
5.
110
100
160
r
6.
17
11
x + 7
x
Example
x 20
3015
UT
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Chapter 7 32 Glencoe Geometry
7-5 Skills Practice
Parts of Similar TrianglesFind x.
1. 2.
7
7
22
x5.25
5.25
15
33
10
x
3. 4.
20
10
x
22
18
12
12.6
x
5. If △RST ∼ △EFG, −−−
SH is an 6. If △ABC ∼ △MNP, −−−
AD is an
altitude of △RST, −−
FJ is an altitude of altitude of △ABC, −−−
MQ is an altitude of
△EFG, ST = 6, SH = 5, and FJ = 7, △MNP, AB = 24, AD = 14, and
find FG. MQ = 10.5, find MN.
JGE
F
HTR
S
C
A
BD PNQ
M
Find the value of each variable.
7. 8.
26
128
m
7
20
24
x
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Lesso
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-5
Chapter 7 33 Glencoe Geometry
Practice
Parts of Similar Triangles
ALGEBRA Find x.
1.
3230
24x
2.
26
25
39
x
3.
402x + 1
25x + 4
4.
5. If △JKL ∼ △NPR, −−−KM is an 6. If △STU ∼ △XYZ,
−−−UA is an
altitude of △JKL, −−PT is an altitude altitude of △STU,
−−ZB is an altitude
of △NPR, KL = 28, KM = 18, and of △XYZ, UT = 8.5, UA = 6, and PT = 15.75, find PR. ZB = 11.4, find ZY.
MJ L
K
TN R
P
YX B
Z
TS A
U
7. PHOTOGRAPHY Francine has a camera in which the distance from the lens to the film is 24 millimeters.
a. If Francine takes a full-length photograph of her friend from a distance of 3 meters and the height of her friend is 140 centimeters, what will be the height of the image on the film? (Hint: Convert to the same unit of measure.)
b. Suppose the height of the image on the film of her friend is 15 millimeters. If Francine took a full-length shot, what was the distance between the camera and her friend?
7-5
x
28
20 30
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Chapter 7 34 Glencoe Geometry
Word Problem Practice
Parts of Similar Triangles
1. FLAGS An oceanliner is flying two
similar triangular flags on a flag pole.
The altitude of the larger flag is three
times the altitude of the smaller flag. If
the measure of a leg on the larger flag is
45 inches, find the measure of the
corresponding leg on the smaller flag.
2. TENTS Jana went camping and stayed
in a tent shaped like a triangle. In a
photo of the tent, the base of the tent is
6 inches and the altitude is 5 inches.
The actual base was 12 feet long. What
was the height of the actual tent?
x
3. PLAYGROUND The playground at
Hank’s school has a large right triangle
painted in the ground. Hank starts
at the right angle corner and walks
toward the opposite side along an angle
bisector and stops when he gets to the
hypotenuse.
A
B
45˚
30 ft
40 ft
50 ft
How much farther from Hank is point B
versus point A?
4. FLAG POLES A flag pole attached to the
side of a building is supported with
a network of strings as shown in the
figure.
AB
C
DF
E
The rigging is done so that AE = EF,
AC = CD, and AB = BC. What is the
ratio of CF to BE?
5. COPIES Gordon made a photocopy of a
page from his geometry book to enlarge
one of the figures. The actual figure that
he copied is shown below.
39 mm
Media
n
Altitude
30 mm
29 mm
The photocopy came out poorly. Gordon
could not read the numbers on the
photocopy, although the triangle itself
was clear. Gordon measured the base of
the enlarged triangle and found it to be
200 millimeters.
a. What is the length of the drawn
altitude of the enlarged triangle?
Round your answer to the nearest
millimeter.
b. What is the length of the drawn
median of the enlarged triangle?
Round your answer to the nearest
millimeter.
7-5
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-5
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Chapter 7 35 Glencoe Geometry
A Proof of Pythagorean Theorem
1. For right triangle ABC with right angle C, and
altitude −−−
CD as shown at the right, name three
similar triangles.
2. List the three similar triangles as headings in
the table below. Use the figure to complete the
table to list the corresponding parts of the three
similar right triangles.
Short Leg
Long Leg
Hypotenuse
3. Use the corresponding parts of these similar triangles and their proportions
to complete the statements in the proof and algebraically prove the
Pythagorean Theorem.
Statements Reasons
1. Right triangle ABC with 1. Given
altitude −−−
CD .
2. 2. Corresponding parts of similar
triangles are in the same ratio.
3. 3. Cross Products Property
4. 4. Addition Property of Equality
5. 5. Substitution
6. 6. Distributive Property
7. 7. Segment addition
8. a2 + b2 = c2 8. Substitution
A
a bh
d e
c
B
C
D
Enrichment7-5
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Chapter 7 36 Glencoe Geometry
You can use a spreadsheet to create a Sierpinski triangle.
Use a spreadsheet to create a Sierpinski triangle.
Step 1 In cell A2, enter 1. In cell A3, enter an equals sign followed by A2 + 1 . This will return the number of iterations. Click on the bottom right corner of cell A2 and drag it through cell A500 to get 500 iterations.
Step 2 In cell B1, enter 0.5. This indicates the midpoints of the segments.
Step 3 In cell C1, enter 1 and in cell D1, enter 0.3.
Step 4 In cell B2, enter an equals sign followed by 3*RAND(). Click on the bottom right corner of cell B2 and drag in through cell B500 to get 500 iterations.
Step 5 In cell C2, enter an equals sign followed by the recursive formula IF(B2<1,(12$B$1)*C1,IF(B2<2,(1-$B$1)*C1+$B$1,(1-$B$1)*C1+2*$B$1)). This will return the x values of the points to be graphed. Click on the bottom right corner of cell C2 and drag through cell C500.
Step 6 In cell D2, enter an equals sign followed by the recursive formula IF(B2<1,(1-$B$1)*D1,IF(B2<2,(1-$B$1)*D1+$B$1,(1-$B$1)*D1)). This will return the y values of the points to be graphed. Click on the bottom right corner of cell D2 and drag through cell D500.
Step 7 To graph the values in columns C and D, first highlight all of the data in the two columns. Next, choose the chart wizard from the toolbar. Select XY (Scatter). Press Next, Next. Then select the Gridlines tab and uncheck the Major gridlines. Then press Next and Finish. This will return the Sierpinski triangle.
Exercises
Analyze your drawing.
1. What happens to your drawing if you have more iterations? Try 1000, 2000, and 5000.
2. Change the 0.5 to 2/3 in cell B1. (Hint: You may need to enter 0.666666 for 2/3.) How does this change the picture?
3. Change 0.3 to 0.6 in cell D1. How does this change the drawing?
4. Enter the following into a new spreadsheet and describe what you see. Step 1: In cell A2, enter the formula = A1. Step 2: In cell B2, enter the formula = A1 + B1. Step 3: Click on the bottom right corner of cell B2 and drag through cell L2. Step 4: First, click on the 2 next to cell A2. Then, click on the bottom left corner of 2
and drag down through cell 12. Step 5: In cell A1, enter a 1 and press ENTER.
Sheet 1 Sheet 2 Sheet 3
Spreadsheet Activity
Fractals
7-5
Example
Less
on
7-6
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Chapter 7 37 Glencoe Geometry
7-6
Identify Similarity Transformations A dilation is a transformation that enlarges or reduces the original figure proportionally. The scale factor of a dilation, k, is the ratio of a length on the image to a corresponding length on the preimage. A dilation with k > 1 is an enlargement. A dilation with 0 < k < 1 is a reduction.
Determine whether the dilation from A to B is an enlargement or a
reduction. Then find the scale factor of the dilation.
Exercises
Determine whether the dilation from A to B is an enlargement or a reduction.
Then find the scale factor of the dilation.
1. y
x
2. y
x
3. y
x
4. y
x
Study Guide and Intervention
Similarity Transformations
Example
a. y
x
B is larger than A, so the dilation is an enlargement.
The distance between the vertices at (-3, 4) and (-1, 4) for A is 2. The distance between the vertices at (0, 3) and (4, 3) for B is 4.
The scale factor is 4 − 2 or 2.
b. y
x
B is smaller than A, so the dilation is a reduction.
The distance between the vertices at (2, 3) and (2, -3) for A is 6. The distance between the vertices at (2, 1) and (2, -2) for B is 3.
The scale factor is 3 −
6 or 1 −
2 .
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Chapter 7 38 Glencoe Geometry
Study Guide and Intervention (continued)
Similarity Transformations
Verify Similarity You can verify that a dilation produces a similar figure by comparing the ratios of all corresponding sides. For triangles, you can also use SAS Similarity.
Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.
Example
a. original: A(-3, 4), B(2, 4), C(-3, -4)
image: D(1, 0), E(3.5, 0), F(1, -4)
Graph each figure. Since ∠A and ∠D are both right angles, ∠A " ∠D. Show that the lengths of the sides that include ∠A and ∠D are proportional to prove similarity by SAS.
Use the coordinate grid to find the lengths of vertical segments AC and DF and horizontal segments AB and DE.
AC
− DF
= 8 −
4 = 2 and AB
− DE
= 5 −
2.5 = 2,
so AC
− DF
= AB −
DE .
Since the lengths of the sides that include ∠A and ∠D are proportional, △ABC ∼ △DEF by SAS similarity.
b. original: G(-4, 1), H(0, 4), J(4, 1), K(0, -2)
image: L(-2, 1.5), M(0, 3), N(2, 1.5), P(0, 0)
Use the distance formula to find the length of each side.
GH = √ ''' 42 + 32 = √ '' 25 = 5
HJ = √ ''' 42 + 32 = √ '' 25 = 5
JK = √ ''' 42 + 32 = √ '' 25 = 5
KG = √ ''' 42 + 32 = √ '' 25 = 5
LM = √ '''' 22 + 1.52 = √ '' 6.25 = 2.5
MN = √ '''' 22 + 1.52 = √ '' 6.25 = 2.5
NP = √ '''' 22 + 1.52 = √ '' 6.25 = 2.5
PL = √ '''' 22 + 1.52 = √ '' 6.25 = 2.5
Find and compare the ratios of corresponding sides.
GH
− LM
= 5 −
2.5 = 2,
HJ −
MN =
5 −
2.5 = 2,
JK
− NP
= 5 −
2.5 = 2,
KC −
PL = 5
− 2.5
= 2.
Since GH
− LM
= HJ
− MN
= JK −
NP = KC
− PL
, GHJK ∼ LMNP.
y
x
y
x
Exercises
Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.
1. A(-4, -3), B(2, 5), C(2, -3), 2. P(-4, 1), Q(-2, 4), R(0, 1), S(-2, -2),
D(-2, -2), E(1, 3), F(1, -2) W(1, -1.5), X(2, 0), Y(3, -1.5), Z(2, -3)
7-6
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Lesso
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-6
Chapter 7 39 Glencoe Geometry
7-6
Determine whether the dilation from A to B is an enlargement or
a reduction. Then find the scale factor of the dilation.
1. y
x
2. y
x
3. y
x
4. y
x
Graph the original figure and its dilated image. Then verify that the dilation is a
similarity transformation.
5. A(–3, 4), B(3, 4), C(–3, –2); 6. F(–3, 4), G(2, 4), H(2, –2), J(–3, –2);
A'(–2, 3), B'(0, 3), C'(–2, 1) F'(–1.5, 3), G'(1, 3), H'(1, 0), J'(–1.5, 0)
Skills Practice
Similarity Transformations
y
x
y
x
7. P(–3, 1), Q(–1, 1), R(–1, –3); 8. A(–5, –1), B(0, 1), C(5, –1), D(0, –3);
P'(–1, 4), Q'(3, 4), R'(3, –4) A'(1, –1.5), B'(2, 0), C'(3, –1.5), D'(2, –3)
y
x
y
x
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Chapter 7 40 Glencoe Geometry
7-6 Practice
Similarity TransformationsDetermine whether the dilation from A to B is an enlargement or a reduction.
Then find the scale factor of the dilation.
1. y
x
2. y
x
3. y
x
4. y
x
5. y
x
6. y
x
Graph the original figure and its dilated image. Then verify that the dilation is a
similarity transformation.
7. Q(1, 4), R(4, 4), S(4, -1), 8. A(-4, 2), B(0, 4), C(4, 2), D(0, -2),
X(-4, 5), Y(2, 5), Z(2, -5) F(-2, 1), G(0, 2), H(2, 1), J(0, -1)
9. FABRIC Ryan buys an 8-foot-long by 6-foot-wide piece of fabric as shown. He wants to cut a smaller, similar rectangular piece that has a scale factor of k = 1 −
4 . If point A(-4, 3)
is the top left-hand vertex of both the original piece of fabric and the piece Ryan wishes to cut out, what are the coordinates of the vertices for the piece Ryan will cut?
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Lesso
n 7
-6
Chapter 7 41 Glencoe Geometry
7-6
1. CITY PLANNING The standard size of a city block in Manhattan is 264 feet by 900 feet. The city planner of Mechlinburg wants to build a new subdivision using similar blocks so the dimensions of a standard Manhattan block are enlarged by 2.5 times. What will be the new dimensions of each enlarged block?
2. STORAGE SHED A local home improvement store sells different sizes of storage sheds. The most expensive shed has a footprint that is 15 feet wide by 21 feet long. The least expensive shed has a footprint that is 10 feet wide by 14 feet long. Are the footprints of the two sheds similar? If so, tell whether the footprints of the least expensive shed is an enlargement or a reduction, and find the scale factor from the most expensive shed to the least expensive shed.
3. FIND THE ERROR Jeremy and Elisa are constructing dilations of rectangle ABCDfor their geometry class. Jeremy draws an enlargement FGHJ that contains the points F (-3, 3) and J(3, -6). Elisa draws a reduction KLMN that contains the points L(-3, 3) and N(-2, 2). Which person made an error in their dilation? Explain.
y
x
4. BANNERS The Bayside High School Spirit Squad is making a banner to take to away games. The banner they use for home games is shown below. If the new banner is to be a reduction of the home
game banner with a scale factor of 1−2
,
what will be the height of the new banner?
13 ft
3.5 ft
5. REASONING Consider the image QRSTof a rectangle WXYZ.
a. Is it possible that point Q and point Wcould have the same coordinates? If so, what must be true about point Q?
b. Is it possible that both points R and Xcould have the same coordinates if points T and Z have the same coordinates? If so, what are the possible values of the scale factor k for the dilation?
Word Problem Practice
Similarity Transformations
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Chapter 7 42 Glencoe Geometry
7-6 Enrichment
Medial and Orthic TrianglesThe medial triangle is the triangle formed by connecting the
midpoints of each side of the triangle. The triangle formed by
A’, B’, and C’ is the medial triangle of triangle ABC.
Use a ruler and compass. Draw the medial triangle for each triangle below.
1. 2.
3. Use the triangles you have created to show that the medial triangle is similar to the
original triangle.
The orthic triangle is the triangle formed by connecting the
endpoints of each of the altitudes of the triangle. The triangle
formed by F, D, and, E is the orthic triangle of triangle ABC.
Use a ruler and compass. Draw the orthic triangle for each triangle below.
1. 2.
3. Use the triangles you have created to show that the orthic triangle is similar to the
original triangle.
'
''
'
''
'
''
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Lesso
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-7
Chapter 7 43 Glencoe Geometry
7-7
Scale Models A scale model or a scale drawing is an object or drawing with lengths proportional to the object it represents. The scale of a model or drawing is the ratio of the length of the model or drawing to the actual length of the object being modeled or drawn.
MAPS The scale on the map shown is 0.75 inches : 6 miles. Find the
actual distance from Pineham to Menlo Fields.
Use a ruler. The distance between Pineham and
Menlo Fields is about 1.25 inches.
Method 1: Write and solve a proportion.
Let x represent the distance between cities.
0.75 in.
− 6 mi
= 1.25 in.
− x mi
0.75 · x = 6 · 1.25 Cross Products Property
x = 10 Simplify.
Method 2: Write and solve an equation.
Let a = actual distance and m = map distance
in inches. Write the scale as 6 mi −
0.75 in. ,
which is 6 ÷ 0.75 or 8 miles per inch.
a = 8 · m Write an equation.
= 8 · 1.25 m = 1.25 in.
= 10 Solve.
The distance between Pineham and Menlo Fields is 10 miles.
Example
map
actual
Exercises
Use the map above and a customary ruler to find the actual distance between
each pair of cities. Measure to the nearest sixteenth of an inch.
1. Eastwich and Needham Beach
2. North Park and Menlo Fields
3. North Park and Eastwich
4. Denville and Pineham
5. Pineham and Eastwich
Study Guide and Intervention
Scale Drawings and Models
Denville
Pineham
Eastwich
North Park
Needham
Beach
Menlo Fields
0.75 in.
6 mi.
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Chapter 7 44 Glencoe Geometry
Study Guide and Intervention (continued)
Scale Drawings and Models
7-7
Use Scale Factors The scale factor of a drawing or scale model is the scale written as a unitless ratio in simplest form. Scale factors are always written so that the model length in the ratio comes first.
SCALE MODEL A doll house that is 15 inches tall is a scale model of
a real house with a height of 20 feet.
a. What is the scale of the model?
To find the scale, write the ratio of a model length to an actual length.
model length
− actual length
= 15 in.
− 20 ft
or 3 in.
− 4 ft
The scale of the model is 3 in.:4 ft
b. How many times as tall as the actual house is the model?
Multiply the scale factor of the model by a conversion factor that relates inches to feet to
obtain a unitless ratio.
3 in.
− 4 ft
= 3 in.
− 4 ft
· 1 ft −
12 in. =
3 −
48 or 1 −
16
The scale factor is 1:16. That is, the model is 1 − 16
as tall as the actual house.
Exercises
1. MODEL TRAIN The length of a model train is 18 inches. It is a scale model of a train
that is 48 feet long. Find the scale factor.
2. ART An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the
height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture
is 14 inches, find the height of the dog.
3. BRIDGES The span of the Benjamin Franklin suspension bridge in Philadelphia,
Pennsylvania, is 1750 feet. A model of the bridge has a span of 42 inches. What is the
ratio of the span of the model to the span of the actual Benjamin Franklin Bridge?
Example
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Lesso
n 7
-7
Chapter 7 45 Glencoe Geometry
7-7
MAPS Use the map shown and a
customary ruler to find the actual
distance between each pair of cities.
Measure to the nearest sixteenth of
an inch.
1. Port Jacob and Southport
2. Port Jacob and Brighton Beach
3. Brighton Beach and Pirates’ Cove
4. Eastport and Sand Dollar Reef
5. SCALE MODEL Sanjay is making a 139 centimeters long scale model of the Parthenon
for his World History class. The actual length of the Parthenon is 69.5 meters long.
a. What is the scale of the model?
b. How many times as long as the actual Parthenon is the model?
6. ARCHITECTURE An architect is making a scale model of an office building he wishes to
construct. The model is 9 inches tall. The actual office building he plans to construct will
be 75 feet tall.
a. What is the scale of the model?
b. What scale factor did the architect use to build his model?
7. WHITE HOUSE Craig is making a scale drawing of the White House on an
8.5-by-11-inch sheet of paper. The White House is 168 feet long and 152 feet wide.
Choose an appropriate scale for the drawing and use that scale to determine the
drawing’s dimensions.
8. GEOGRAPHY Choose an appropriate scale and construct a scale drawing of each
rectangular state to fit on a 3-by-5-inch index card.
a. The state of Colorado is approximately 380 miles long (east to west) and 280 miles
wide (north to south).
b. The state of Wyoming is approximately 365 miles long (east to west) and 265 miles
wide (north to south).
Skills Practice
Scale Drawings and Models
Port Jacob
Eastport Brighton Beach
Pirates’ Cove
Southport
Sand Dollar Reef
0.5 in.
20 mi
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Chapter 7 46 Glencoe Geometry
Practice
Scale Drawings and Models
7-7
MAPS Use the map of Central New Jersey shown and an inch ruler to find the
actual distance between each pair of cities. Measure to the nearest sixteenth of
an inch.
1. Highland Park and Metuchen
2. New Brunswick and Robinvale
3. Rutgers University Livingston
Campus and Rutgers University
Cook–Douglass Campus
4. AIRPLANES William is building a
scale model of a Boeing 747–400 aircraft.
The wingspan of the model is approximately 8 feet 10 1−16
inches. If the scale factor of the
model is approximately 1:24, what is the actual wingspan of a Boeing 747–400 aircraft?
5. ENGINEERING A civil engineer is making a scale model of a highway on ramp.
The length of the model is 4 inches long. The actual length of the on ramp is 500 feet.
a. What is the scale of the model?
b. How many times as long as the actual on ramp is the model?
c. How many times as long as the model is the actual on ramp?
6. MOVIES A movie director is creating a scale model of the Empire State Building to
use in a scene. The Empire State Building is 1250 feet tall.
a. If the model is 75 inches tall, what is the scale of the model?
b. How tall would the model be if the director uses a scale factor of 1:75?
7. MONA LISA A visitor to the Louvre Museum in Paris wants to sketch a drawing
of the Mona Lisa, a famous painting. The original painting is 77 centimeters by
53 centimeters. Choose an appropriate scale for the replica so that it will fit on a
8.5-by-11-inch sheet of paper.
1 in.
1.88 mi
HighlandPark
Metuchen
NewBrunswick
Robinvale
RutgersUniv-Cook-Douglass
Campus
RutgersUniv-Livingston
Campus
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Lesso
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-7
Chapter 7 47 Glencoe Geometry
7-7
1. MODELS Luke wants to make a scale
model of a Boeing 747 jetliner. He wants
every foot of his model to represent
50 feet. Complete the following table.
Part
Actual
length (in.)
Model
length (in.)
Wing Span 2537
Length 2782
Tail Height 392
(Source: Boeing)
2. PHOTOGRAPHS Tracy is 4 feet tall and
her father is 6 feet tall. In a photograph
of the two of them standing side by side,
Tracy’s image is 2 inches tall.
6 ft
4 ft
Although their images are much
smaller, the ratio of their heights
remains the same. How tall is Tracy’s
father’s image in the photo? What is
the scale of the photo?
3. TOWERS The Tokyo Tower in Japan is
currently the world’s tallest self-
supporting steel tower. It is 333 meters
tall.
a. Heero builds a model of the Tokyo
Tower that is 2775 millimeters tall.
What is the scale of Heero’s model?
b. How many times as tall as the actual
tower is the model?
4. PUPPIES Meredith’s new Pomeranian
puppy is 7 inches tall and 9 inches long.
She wants to make a drawing of her new
Pomeranian to put in her locker. If the
sheet of paper she is using is 3 inches by
5 inches, find an appropriate scale factor
for Meredith to use in her drawing.
5. MAPS Carlos makes a map of his
neighborhood for a presentation. The
scale of his map is 1 inch:125 feet.
a. How many feet do 4 inches represent
on the map?
b. Carlos lives 250 feet away from
Andrew. How many inches separate
Carlos’ home from Andrew’s on
the map?
c. During a practice run in front of his
parents, Carlos realizes that his map
is far too small. He decides to make
his map 5 times as large. What would
be the scale of the larger map?
Word Problem Practice
Scale Drawings and Models
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Chapter 7 48 Glencoe Geometry
7-7
Area and Volume of Scale Models and Drawings
You have already learned about changes of length measures between scale models and the object that is being modeled. The areas and volumes of scale models and drawings also change, but by multiples different than the “scale factor.”
Yuan is making a scale model of a cylinder. The actual cylinder has
a radius of r inches and a height of h inches. The scale factor of the model is 1:2.
What is the ratio of volumes of the model cylinder to the actual cylinder?
The volume formula for a cylinder is V = πr2h. The actual cylinder’s volume is πr2h.
If the cylinder is scaled down by a factor of 1:2, the new radius will be 1 − 2 r and the new
height will be 1 − 2 h.
V = π ( 1 − 2 r)
2
( 1 − 2 h)
= 1 − 8 πr2h
The model’s volume is 1 − 8 of the actual volume.
Exercises
1. Consider a painting on a 22-inch-by-28-inch canvas. Suppose you wish to make a 1:2 scale model of the painting for art class. What is the ratio of areas of the model painting to the actual painting?
(Area = Length × Width)
2. The Parks and Recreation Office is planning a new circular playground with a radius of 30 feet. Before they can construct the playground, they ask an architect to create a 1:20 scale model of the proposed playground such that the new radius is 1.5 feet. What is the ratio of areas of the model playground to the proposed actual playground?
(Area = π × (radius)2)
3. A refrigerator manufacturer uses a 7-foot-by-3-foot-by-3-foot box for its standard model. The marketing team suggests the manufacturer start selling a smaller, lower-priced refrigerator with a scale factor of 4:5 to the standard model. If the box is reduced by a similar scale, what is the ratio of volumes of the new, smaller box to the current box?
(Volume = length × width × height)
4. Consider a cube with side lengths x. If each side of the cube is scaled by a factor of 1:y, what is the ratio of volumes of the model cube to the actual cube?
(Volume = length × width × height)
Enrichment
Example
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Assessment
Chapter 7 49 Glencoe Geometry
8.
7
Read each question. Then fill in the correct answer.
1. A B C D
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
7. A B C D
Multiple Choice
Student Recording Sheet
Use this recording sheet with pages 610–611 of the Student Edition.
Record your answer in the blank.
For gridded response questions, also enter your answer in the grid by writing
each number or symbol in a box. Then fill in the corresponding circle for that
number or symbol.
8. (grid in)
9.
10.
11.
12.
13.
14. (grid in)
15.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Extended Response
Record your answers for Question 16 on the back of this paper.
14.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Short Response/Gridded Response
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SCORE
Chapter 7 50 Glencoe Geometry
7
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not show
how he or she arrived at the answer, the student will be awarded only 1 credit.
All extended-response questions require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for
all parts of the question. For example, if a question has three parts, the correct
response to one or two parts of the question that required work to be shown is not
considered a fully correct response.
• Students who use trial and error to solve a problem must show their method.
Merely showing that the answer checks or is correct is not considered a complete
response for full credit.
Exercise 11 Rubric
Rubric for Extended-Response
Score Speci! c Criteria
4 An understanding that using proportional parts created by parallel lines is
shown by the student creating the proportion XQ
− QZ
= YR −
RZ . The correct
substitutions are made for part b to determine the length of −−
RZ , or 16 units.
The correct substitutions are made for part c to determine the length of −−
XY , or 9.5 units.
3 A generally correct solution, but may contain minor flaws in reasoning or computation.
2 A partially correct interpretation and/or solution to the problem.
1 A correct solution with no evidence or explanation.
0 An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given.
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NAME DATE PERIOD
7
SCORE
SCORE
Chapter 7 51 Glencoe Geometry
7
1. The ratios of measures of the angles in △ABC is 4:13:19. Find
the measures of the angles.
2. SCHOOL ELECTIONS Henrietta conducted a random survey
of 60 students and found that 36 are planning to vote for her
as class president. If there are 460 students in Henrietta’s
class, predict the total number of students who will vote for
her as class president.
3. Are any of the three triangles
similar? If so, write
the appropriate similarity
statement.
4. If △ABC ∼ △DEC, find x and the
scale factor of △ABC to △DEC.
5. MULTIPLE CHOICE In a rectangle, the ratio of the length to
the width is 5:2, and its perimeter is 126 centimeters. Find the
width of the rectangle.
A 9 cm B 18 cm C 45 cm D 50.4 cm
D
E
CB
A
20
25
3x - 22x
BP X Y
Z
Q
R
A
C
5
4 8 8 8
10
4
1.
2.
3.
4.
5.
For Questions 1 and 2, determine whether each pair of
triangles is similar. Justify your answer.
1. 2.
3. Identify the similar triangles in the figure,
then find the value of x.
4. Determine whether −−−
MN ‖ −−
KL
Justify your answer.
5. In △ABC, −−−
DE is parallel to −−
AC and DE = 10. Find the length
of −−
AC if −−−
DE is the midsegment of △ABC .
1.
2.
3.
4.
5.
Chapter 7 Quiz 1(Lessons 7-1 and 7-2)
Chapter 7 Quiz 2(Lessons 7-3 and 7-4)
8
A
B D
E
F
C 4
6x
20
15
98
10 12
41°
52°41°
87°
J
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2
3
9
L
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7
SCORE
SCORE
Chapter 7 52 Glencoe Geometry
7
For Questions 1–3 △ABC ∼ △DEF, and −−
BE bisects ∠ABC.
1. Find the length of −−
XC to the nearest tenth.
2. What is the relationship between the corresponding altitudes
−− BX and
−− EY ?
3. Find the length of −−
EY to the nearest tenth.
4. Determine if the dilation from A and B is an enlargement or reduction. Then find the scale factor of the dilation.
5. Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation. original: A(-1, 4), B(1, 4), C(4, -2), D(-4, -2)
image: F(-3, 0), G (- 7 −
3 , 0) , H (- 4 −
3 , -2) , J(-4, -2)
1.
2.
3.
4.
5.
1. GARDENS The model of a circular garden is 8 inches in diameter. The actual garden will be 20 feet in diameter. Find the ratio of the diameter of the model to the diameter of the actual garden.
2. PHOTOS A 4-inch by 6-inch photograph, set vertically, is enlarged to make a poster 22 inches wide. How tall is the poster?
3. TICKETS Sofia is making a copy of a ticket from the school play to put in her memory album. The original ticket is 7 inches long and 5 inches wide. Her copy is 2 inches long.
What is the scale of the copy of the ticket?
4. MULTIPLE CHOICE An NCAA regulation size lacrosse field measures 110 yards long by 60 yards wide. Which of the following would be an appropriate scale to construct a scale drawing of a lacrosse field so it would best fit on a 8.5-by-11-inch sheet of paper? (1 yd = 36 in.)
A 1:250 B 1:255 C 1:355 D 1:365
1.
2.
3.
4.
Chapter 7 Quiz 3(Lessons 7-5 and 7-6)
Chapter 7 Quiz 4(Lesson 7-7)
12 14 cm
2 cm
8 cm
X
y
8
y
x
Assessm
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Chapter 7 53 Glencoe Geometry
7
1. Polygon ABCD is similar to polygon PQRS. Which proportion must be true?
A AC
− AD
= PQ
− PS
B BC
− CD
= QR
− RS
C AB −
BD =
PQ −
QR D
CD −
AB =
PQ −
RS
2. This fall, 126 students participated in the soccer program, while 54 played
volleyball. What was the ratio of soccer players to volleyball players?
F 3 −
4 G
3 −
7 H 4 −
3 J
7 −
3
3. The ratio of the measures of the angles of a triangle is 2:3:10. What is the
least angle measure?
A 12 B 15 C 24 D 36
4. Find the value of x.
F 2 H 6
G 4.8 J 6.4
5. Rectangle ABCD ∼ rectangle EFGH, the perimeter of ABCD is
54 centimeters and the perimeter of EFGH is 36 centimeters. What is the
scale factor of ABCD to EFGH?
A 2 − 3 B
3 −
2 C
3 −
5 D
5 −
3
1.
2.
3.
4.
5.
Part I Write the letter for the correct answer in the blank at the right of each question.
Chapter 7 Mid-Chapter Test(Lessons 7-1 through 7-4)
10 8
x
D
E
ACB18
6.
7.
8.
9.
10.
Part II
For Questions 6 and 7, determine whether each pair of
triangles is similar. Justify your answer.
6. 7.
8. Determine whether −−−
MN ‖ −−
KL . Justify your answer.
4525181085°85°6
415
10
J
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2
3
9
L
K
20
12
15DE
B
A
C
9. Find DE.
10. RECTANGLES A rectangle has a perimeter of 14 inches. A
similar rectangle has a perimeter of 10 inches. If the length of
the larger rectangle is 4 inches, what is the length of the
smaller rectangle? Round to the nearest tenth.
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Chapter 7 54 Glencoe Geometry
7
Choose the correct term to complete each sentence.
1. If there are 15 girls and 9 boys in an art class, the (ratio, scale factor) of girls to boys in the class is 5:3.
2. If △ABC ∼ △DEF, AB = 10, and DE = 2.5, then the (scale factor, proportion) of △ABC to △DEF is 4:1.
Choose from the terms above to complete each sentence.
3. In △LMN, P lies on −−−
LM and Q lies on −−−
LN . If PQ = 1 − 2 MN,
−−− PQ
is called a(n) .
4. The product of the in the equation 3 − x = 24
− 30
is 90.
5. The product of the in the equation 3 − x = 24
− 30
is 24x.
Write whether each sentence is true or false. If false,
replace the underlined term to make a true sentence.
6. If quadrilaterals ABCD and WXYZ have corresponding angles congruent and corresponding sides proportional, they are called cross products.
7. The equation 3 − x = 24
− 30
is called a(n) scale factor.
8. In a proportion, the cross products of the extremes equals the cross product of the means.
Define each term in your own words.
9. equality of cross products
10. midsegment
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
cross products
dilation
enlargement
extremes
means
midsegment of a triangle
proportion
ratio
reduction
scale
scale drawing
scale factor
scale model
similar polygons
similarity transformation
Chapter 7 Vocabulary Test
?
?
?
Assessment
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Chapter 7 55 Glencoe Geometry
7
Write the letter for the correct answer in the blank at the right of each question.
1. There are 15 plums and 9 apples in a fruit bowl. What is the ratio of apples
to plums?
A 3:5 B 3:8 C 5:3 D 8:3
2. The scale drawing of a porch is 8 inches wide by 12 inches long. If the actual
porch is 12 feet wide, what is the length of the porch?
F 8 ft G 10 ft H 16 ft J 18 ft
3. Solve 5 −
6 = 4 − x .
A 4.6 B 4.8 C 5 D 7
4. A quality control technician checked a sample of 30 bulbs. Two of the bulbs
were defective. If the sample was representative, find the number of bulbs
expected to be defective in a case of 450.
F 24 G 30 H 36 J 45
5. Find the triangle similar to △ABC at the right.
A C
B D
6. Find the value of x if △ABC ∼ △JKL.
F 10 H 25
G 14 J 29
7. Quadrilateral ABCD ∼ quadrilateral PQRS. If AB = 10, BC = 6, PS = 12,
and QR = 4, find the scale factor of ABCD to PQRS.
A 1 − 2 B
3 −
2 C
5 −
3 D
5 −
6
8. Quadrilateral ABCD ∼ quadrilateral EFGH.
Find the value of x.
F 15 H 25
G 20 J 30
9. Which theorem or postulate can be used to prove
that these two triangles are similar?
A AA B SAS C SSA D SSS
10. Find MN.
F 5 1 − 3 G 6
3 −
4 H 7 J 12
2210
24
15
36
39
6
84
27°63°
B
C
D
A
F
E
H
G60° 120°
80°100°4x°
A C
B J L
K18
6 9x - 2
4
35
5
12
3
5
12
13
CB
A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Chapter 7 Test, Form 1
35°
8
96
35°
Q
PM
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Chapter 7 56 Glencoe Geometry
7
11. A 5-foot tall student cast a 4-foot shadow. If the tree next to her cast a 44-foot
shadow, what is the height of the tree?
A 35 1 − 5 ft B 45 ft C 51 1 −
2 ft D 55 ft
12. In △ABC, −−−
DE ‖ −−
AC . If AD = 12, BD = 3, and CE = 10,
find BE.
F 1 H 2
G 1 1 − 2 J 2 1 −
2
13. What is the scale factor of the dilation of A to B?
A 1 C 2
B 3 −
2 D 6
14. △FGH ∼ △PQR, FG = 6, PQ = 10, and the perimeter
of △PQR is 35. What is the perimeter of △FGH?
F 21 G 27 H 31 J 58 1 − 3
15. Find the value of x.
A 14 C 16
B 15 D 18
16. △LMN ∼ △XYZ with altitudes −−
KL
and −−−
WX . Find KL.
F 6 H 9
G 7 J 19
17. Find the value of x.
A 5 C 6 1 − 2
B 6 D 7 1 − 2
18. Find the value of x.
F 16 H 20
G 18 J 21
19. Nathan is building a model of his father’s sailboat with a scale factor of 1 − 32
.
The actual sail is in the shape of a right triangle with a base of 8 meters and
a hypotenuse of 13 meters. What will be the approximate perimeter of the
sail on the model boat?
A 32 cm B 48.81 cm C 65.62 cm D 97.65 cm
Bonus In △ABC, AB = 10, BC = 16,
−−−
DE ⊥ −−
AC , and DE = 6. Find CD.
15
1824
x
16
10
129x
28 123
K
L X
M YWZN
16
10
24x
11.
12.
13.
14.
15.
16.
17.
18.
19.
Chapter 7 Test, Form 1 (continued)
C B
A
E
D
12
10
3
106
B C
D
E
A
16
B:
−2−1
y
x
2
1
−2
−11 2 3 4 5 6
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NAME DATE PERIOD
SCORE
Chapter 7 57 Glencoe Geometry
7
Write the letter for the correct answer in the blank at the right of each question.
1. Of the 240 students eating lunch, 96 purchased their lunch and the rest
brought a bag lunch. What is the ratio of students purchasing lunch to
students bringing a bag lunch?
A 2:3 B 2:5 C 3:2 D 5:2
2. In a rectangle, the ratio of the width to the length is 4:5. If the rectangle is
40 centimeters long, find its width.
F 32 cm G 36 cm H 44 cm J 50 cm
3. A postage stamp 25 millimeters wide and 40 millimeter tall is enlarged to
make a poster. The poster is 4 feet wide. Find the height of the poster.
A 2.5 ft B 5.25 ft C 5.8 ft D 6.4 ft
4. Find the polygon that is similar to ABCD.
F H
G J
5. If △PQR ∼ △STU, find the value of x.
A 4.4 C 24.6
B 7 D 35
6. If ABCD ∼ EFGH, find the value of x.
F 18.75 H 22.75
G 20 J 28
7. △ABC ∼ △LMN, AB = 18, BC = 12, LN = 9, and LM = 6. What is the scale
factor of △ABC to △LMN?
A 9 −
2 B
3 −
2 C
3 −
1 D 2 −
1
8. Name the theorem or postulate that can be used to
prove that these triangles are similar.
F AA Similarity H SAS Similarity
G SSS Similarity J SSA Similarity
For Questions 9 and 10, refer to the figure at the right.
9. Identify the true statement.
A △PQR ˜ △RST C △PQR ˜ △TSR
B △PQR ˜ △STR D △PQR ˜ △TRS
10. Find the value of x.
F 2 1 − 2 G 3 H 3 1 −
2 J 4
2 6
2–3
2
15
18
4x
2
21–2
3
T
R
P
Q
S
14
4
3
7
16
30
10
x - 4
A
BC
DE H
GF
22°123°
5x°12 8
4.5
R U
S
TQ
P
8
8
18
6 4
12
A D
B C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Chapter 7 Test, Form 2A
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Chapter 7 58 Glencoe Geometry
7 Chapter 7 Test, Form 2A (continued)
11. A 24-foot flagpole cast a 20-foot shadow. At the same time, the building next
to it cast an 85-foot shadow. Find the height of the building.
A 70 5 −
6 ft B 89 ft C 96 1 −
6 ft D 102 ft
12. Find QT.
F 15 H 19
G 17 J 21
13. Find the value of x so that −−
ST ‖ −−
PR .
A 4 C 6
B 4 1 − 2 D 6 1 −
2
14. Find the value of y.
F 4 −
3 H
7 −
3
G 2 J 3
15. If △KLM ∼ △XYZ, find the perimeter of △XYZ.
A 40 C 45
B 42 D 48
16. △ABC ∼ △JKL with altitudes −−
BX and −−
KY .Find BX.
F 19.2 H 24.6
G 21 J 28
17. Find the value of x.
A 4 C 6
B 5 D 8
18. What is the scale factor of the dilation of A to B?
F 2 H 1
G 3 −
2 J
1 −
2
Bonus Find the value of x.
128
x + 2 x
32
XCA
B10
6
YLJ
K
9
X Z
Y4
K M
L7
9
6
9
2y
1–3y + 2
25
5
34x - 3QR
P
S
T
24
40
35RQ
PS
T
11.
12.
13.
14.
15.
16.
17.
18.
B:
12
4 x
−3−2−1
y
x
4
3
2
1
−4
−4
−3
−2
−11 2 3 4
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NAME DATE PERIOD
SCORE
Chapter 7 59 Glencoe Geometry
7 Chapter 7 Test, Form 2B
Write the letter for the correct answer in the blank at the right of each question.
1. Given the choice between doing an oral and a written report, 18 of the 28
students chose to do an oral report. Find the ratio of written to oral reports.
A 5:9 B 9:5 C 9:14 D 14:9
2. A model of a lighthouse has diameter 8 inches and height 18 inches. If the
actual diameter of the lighthouse is 20 feet, find its actual height.
F 30 ft G 35 ft H 45 ft J 50 ft
3. The three sides of a triangle are in the ratio 2:4:5. If the shortest side of the
triangle is 4 meters long, find the perimeter.
A 17 m B 22 m C 32 m D 40 m
4. Find the polygon that is similar to ABCD.
F H
G J
5. If △ABC ∼ △DEF, find m∠C.
A 54 C 67
B 59 D 69
6. Quadrilateral JKLM ∼ quadrilateral WXYZ, JK = 15, LM = 10, XY = 6, and
WX = 9. Find KL.
F 8 G 10 H 11 J 12
7. △LMN ∼ △RST, LN = 21, MN = 28, and the scale factor of △RST to △LMN
is 4 − 3 . Find ST.
A 15 3 −
4 B 21 C 28 D 37 1 −
3
8. Name the theorem or postulate that can be used to prove that these triangles
are similar.
F AA Similarity H SSA Similarity
G SAS Similarity J SSS Similarity
For Questions 9 and 10, refer to the figure at the right.
9. Identify the similar triangles.
A △LMN ∼ △MPQ C △LMN ∼ △QPM
B △LMN ∼ △QMP D △LMN ∼ △PQM
10. Find LM.
F 16 G 17 H 18 J 20
22
18
6
17
14
6
1510 12
L
N
MP
Q
20
8
11.2
28
54°67°
67°
DECA
FB
12
15
5
12
15
54
A B
D C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
30
24
8
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NAME DATE PERIOD
Chapter 7 60 Glencoe Geometry
7
11.
12.
13.
14.
15.
16.
17.
18.
B:
11. A 6-foot-tall fence post cast a 2 1 − 2 -foot shadow. At the same time, a nearby
clock tower cast a 35-foot shadow. What is the height of the tower?
A 37 1 − 2 ft B 71 ft C 78 ft D 84 ft
12. Find CE.
F 25 H 27
G 26 J 28
13. Find FH so that −−−
GH ‖ −−−
DE .
A 4 C 6
B 5 D 7
14. Find the value of x.
F 4 H 9
G 6 J 12
15. What is the scale factor of the dilation of A to B?
A 1 −
2 C
4 −
3
B 3 −
4 D 2
16. △ABC ∼ △XYZ with altitudes −−
AP and
−−− XQ . Find AP.
F 11 1 − 4 H 15 1 −
4
G 14 J 20
17. Find the value of x.
A 7 C 9
B 8 D 10
18. Find the value of y.
F 3 3 −
4 H 6
G 4 J 7 1 − 2
Bonus Find CE.6
5
4
39
A
B
C
D
E
6
21–4
16
y
R T
SU
40
16
x + 2
3x
125
Q
X
YZ
27
P
A
B C
5
8
2x
x + 3
9
10
15D
G
FE H
8
20
EB C
DA
35
Chapter 7 Test, Form 2B (continued)
−3−2−1
y
x
4
3
2
1
−4−1
1 2 3 4
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NAME DATE PERIOD
SCORE 7
1. Of the 300 television sets sold at an electronics store last
month, 90 were flat-screen TVs. What is the ratio of
flat-screen TVs to other TVs sold last month?
2. Determine whether △ABC ∼ △DEF. Justify your answer.
22.5
15 1510
A
B
C DE
F
3. When a 5-foot vertical pole casts a 3-foot 4-inch shadow, an
oak tree casts a 20-foot shadow. Find the height of the tree.
4. Quadrilateral ABCD ∼ quadrilateral WXYZ, AB = 15,
BC = 27, BC = 27, and the scale factor of WXYZ to
ABCD is 2 − 3 . Find XY.
5. The blueprint for a swimming pool is 8 inches by 2 1 − 2 inches.
The actual pool is 136 feet long. Find the width of the pool.
6. Find CD.
1.8
2.46C E
G
F
D
7. If quadrilateral ABCD ∼ quadrilateral PQRS, find BC.
28
106.5
R
S P
Q B
A
C
D
8. Is the dilation a similarity
transformation? Verify your answer.
9. △ABC ∼ △XYZ, AB = 12, AC = 16, BC = 20, and XZ = 24.
Find the perimeter of △XYZ.
For Questions 10 and 11, use the figure.
10. Identify the similar triangles.
11. Find the value of x.15 2x - 4
x
6
P
Q
R S
T
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 Test, Form 2C
Chapter 7 61 Glencoe Geometry
−6−4−2
y
x
8
6
4
2
−22 4 6 8 10
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NAME DATE PERIOD
7
12. If △ABC ∼ △PQR and −−−
BM and −−−
QN are medians, find BM.
11
4.43.8
A C P R
Q
B
M N
13. The ratio of the measures of the three sides of a triangle is
3:4:6. If the perimeter is 91, find the length of the longest
side.
14. If △RST ∼ △UVW, find m∠W.
15. In △ABC, −−−
AX bisects ∠BAC.
Find the value of x.
16. Find the value of y so that −−−
MN || −−−
BC .
17. △ABC ∼ △LMN, and −−−
AD and 36
208
D
A
CB M P
L
N
−−
LP are altitudes. Find AD.
18. Find the value of x. 8
18
2x - 2
13.5
Bonus Find EG. 18
10
12
B
F
D E
G
C
A
28
4x - 5
2x
8
6
A C
X
B
12.
13.
14.
15.
16.
17.
18.
B:
Chapter 7 Test, Form 2C (continued)
Chapter 7 62 Glencoe Geometry
85°
48°R T
S
U W
V
18
8y4
y
B
CAN
M
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NAME DATE PERIOD
SCORE 7
1. Of the 112 students in the marching band, 35 were in the
drum section. What is the ratio of drummers to other
musicians in the band?
2. Determine whether quadrilateral ABCD ∼ quadrilateral
EFGH. Justify your answer.
A
9
7
14 17
9 8.5
13.5
12B
C
DH G
FE
3. When a 9-foot tall garden shed cast a 5-foot 3-inch shadow,
a house cast a 28-foot shadow. Find the height of the house.
4. △ABC ∼ △FGH, AB = 24, AC = 16, GH = 9, and FH = 12.
Find the scale factor of △ABC to △FGH.
5. The model of a suspension bridge is 18 inches long and
2 inches tall. If the length of the actual bridge is 1650 feet,
find its height.
6. Find GP.
2.73.3
4.5
F H
Q
G
P
7. If △JKL ∼ △PQR,
find the value of x.
8. Is the dilation a similarity
transformation? Verify your answer.
9. △ABC ∼ △PQR, AB = 18, BC = 20, AC = 22, and QR = 25.
Find the perimeter of △PQR.
For Questions 10 and 11, use the figure.
20
x
6
Y Z
X
M
N
16 10. Identify the similar triangles.
11. Find MN.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 Test, Form 2D
Chapter 7 63 Glencoe Geometry
−6−4−2
y
x
8
6
4
2
−22 4 6 8 10
35
14
6
x
J L
PQ
R
K
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NAME DATE PERIOD
7
12. If △FGH ∼ △LMN and −−
AF and −−
BL are medians, find BL.
16.8 4.8
7.7
F H L
MB
N
G
A
13. The ratio of the measures of the three angles of a triangle is
3:4:8. Find the measure of the largest angle.
14. If quadrilateral DEFG ∼ quadrilateral WXYZ, find m∠Y.
E F Z W
X
YG
D
68° 85°
82°125°
15. In △PQR, −−−
QS bisects ∠PQR.
Find the value of x.
16. Find the value of x so that −−−
PQ || −−−
FH .
17. If △FGH ∼ △JKL, find GX.
X Y
K
F H JL
27 12 21–2
G
18. Find the value of y.
42 2y
12 16
Bonus Find FG.
12.
13.
14.
15.
16.
17.
18.
B:
Chapter 7 Test, Form 2D (continued)
Chapter 7 64 Glencoe Geometry
P Q
R
S3x - 1
32
40
2x + 3
63
3x2x - 1
F H
Q
G
P
2.8 3.24.2
8 7
A
B F
GEC
D
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NAME DATE PERIOD
SCORE 7
1. In an orchard of apple and peach trees, 3 −
7 of the trees are
peaches. What is the ratio of apple trees to peach trees?
2. Determine whether trapezoid ABCD ∼ trapezoid PQRS.
Justify your answer.
9.6
15.6
12.47.8
9
15
6
23.4D
R S
PQ
C
A
B
3. In △ABC, m∠A = 51, AB = 14, and AC = 20. In △DEF,
m∠D = 51, DE = 16.8, and DF = 24. Determine whether
△ABC ∼ △DEF. Justify your answer.
4. A painting that is 48 inches by 12 inches is reduced to fit on a
canvas that is 30 centimeters by 10 centimeters. Find the
maximum dimensions of the reduced painting.
5. Find the value of x. 6
4.8
6.5K L
J
N
M
2x
6. If △ABC ∼ △XYZ, find y.
17.5A C
B
2y
14X Z
Y
y + 3
7. The ratio of the measures of the sides of a triangle is 2:5:6. If
the length of the longest side is 48 inches, find the perimeter.
8. Find m∠ I.
F
G
HI
J
45°
53°
9. △ABC ∼ △DEF, AB = 8, BC = 13, AC = 15, and DF = 20.
Find the perimeter of △DEF.
10. △ABC ∼ △JKL, AB = 12, BC = 18.4, KL = 6.9, and JL = 5.6.
Find the scale factor of △ABC to △JKL.
11. Find the value of y. y + 84y - 7
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 Test, Form 3
Chapter 7 65 Glencoe Geometry
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NAME DATE PERIOD
7
12. Find SR.
30 12
Q
RPS
40
For Questions 13 and 14, △FGH ∼ △JKL.
12x
F H
G7.5
4.5
J L
K
13. Find the value of x.
14. Find the ratio of the perimeter of △FGH to the perimeter of △JKL.
15. Find AD so that −−−
DE || −−
AB .
A B
ED
C
2x - 4 3x
8x5x
16. A triangle with coordinates A(0, 0), B(4, 0), and C(0, 4) is enlarged by a factor of 2. What are the coordinates of the image?
17. When a 15-foot tall climbing wall cast a 20-foot shadow, a building cast a 32-foot shadow. Find the height of the building.
18. If △ABC ∼ △EFG and −−−
BD and −−−
FH are medians, find BD.
HE G
F2x - 5
75
1–4
x + 5
DA C
B
Bonus The ratio of the lengths of the
sides of △ABC is 5:2 1 − 2 :4. The
scale factor of △ABC to △DEC is 5:2, and the scale factor of △DEC to △FEG is 1:4.
−−− BC is
the shortest side and −−
AB is the longest side of △ABC. Find FG.
12.
13.
14.
15.
16.
17.
18.
B:
Chapter 7 Test, Form 3 (continued)
Chapter 7 66 Glencoe Geometry
10
A
BC
D E
G
F
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NAME DATE PERIOD
SCORE 7
Demonstrate your knowledge by giving a clear, concise solution to
each problem. Be sure to include all relevant drawings and justify
your answers. You may show your solution in more than one way or
investigate beyond the requirements of the problem.
1. Write a possible proportion if the extremes are 3 and 10.
2. △ABC and △WXY are isosceles triangles.
a. Write a possible ratio for the sides of △ABC if its perimeter is
42 inches.
b. Name possible measures for the sides of △ABC using your answer to
part a.
c. If △WXY has a perimeter of 28 and △ABC has sides with the measures
you gave in part b, what must be the measure of the sides of △WXY so
that △WXY ∼ △ABC?
3. Write as many triangle similarity statements as possible for the figure
below. How do you know that these triangles are similar?
A B C D
IE
F
G
H
4. Sketch two triangles that are not similar, but have one pair of
corresponding angles congruent and two pairs of corresponding sides
proportional. Label the corresponding angles and the proportional sides.
5. Draw △XYZ inside △PQR with half the perimeter of △PQR. Explain your
process and why it works.
Chapter 7 Extended-Response Test
Chapter 7 67 Glencoe Geometry
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NAME DATE PERIOD
SCORE 7
1. Find the length of −−
YZ . (Lesson 1-2) X Z
5.5 in.
3.6 in. Y
A 1.9 in. C 7.2 in. B 5.3 in. D 12.5 in.
2. Given: 3b + 4 < 16 Conjecture: b > 0Which of the following would be a counterexample? (Lesson 2-1)
F b = -1 G b = 0 H b = 3.5 J b = 4
3. Find the plane that is parallel to
R
P
Q
ST
U
plane PTU. (Lesson 3-1)
A plane QRU C plane PQS B plane QRS D plane SPU
4. Find m∠1. (Lesson 3-2)
(3x + 5)°
(125 - 7x)°
1 F 5 H 41 G 12 J 44
5. Which statement must be true in order to D
A C
B
prove △ABC % △DCB by SAS? (Lesson 4-4)
A −−−
CB bisects ∠ABD. B ∠BCA % ∠CBD C ∠BDC % ∠CAB D
−− AB %
−−− BC
6. In an indirect proof, you assume that the conclusion is false and then find a(n) ? . (Lesson 5-4)
F assumption H truth value G contradiction J conditional statement
7. Demont and Tony are competing to see whose house is the tallest. Early in the afternoon, Tony, who is 4 feet tall, measured his shadow to be 9.6 inches and the shadow of his house to be 62.4 inches. Later in the day, Demont, who is 5 feet tall, measured his shadow to be 15.6 inches and the shadow of his house to be 62.4 inches. Who lives in the taller house? (Lesson 7-3)
A Demont B Both houses are the same height. C Tony D There is not enough information.
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
1.
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
7. A B C D
Standardized Test Practice(Chapters 1-7)
Chapter 7 68 Glencoe Geometry
A B C D
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NAME DATE PERIOD
7
8. Find the coordinates of the midpoint of −−
AB for A(-24, 15) and B(13, -31). (Lesson 1-3)
F (-18.5, -23) G (-11, -16) H (-5.5, -8) J (10.5, 23)
For Questions 9 and 10, use the figure D E
G F
at the right.
9. The perimeter of rectangle DEFG is 176, EF = h, and DE = 7h. What is the value of h? (Lesson 1-6)
A 11 C 22 B 15 D 77
10. What is the area of the rectangle DEFG? (Lesson 1-6)
F 88 units2 G 225 units2 H 513 units2 J 847 units2
11. What is the slope-intercept form for the line y + 7 = 4(x-10)? (Lesson 3-4)
A y = 4x - 47 B 4x - y = 47 C 4x = y + 17 D 4 x − y = 17
12. Which of the following is the equation of a line parallel to the line passing through (4, -3) and (8, 5)? (Lesson 3-4)
F y = x + 2 G 2y = 9x + 4 H 2y = 2x + 4 J y = 2x + 9
8. F G H J
9. A B C D
10. F G H J
11. A B C D
12. F G H J
13. Find m∠2. (Lesson 3-2)
52°
12
34
14. △LMN is equilateral, LM is one more than three times a number, MN is nine less than five times the number, and NL is eleven more than the number. Find LM. (Lesson 4-1)
Part 2: Gridded Response
Instructions: Enter your answer by writing each digit of the
answer in a column box and then shading in the appropriate circle
that corresponds to that entry.
13.
14.
Standardized Test Practice (continued)
Chapter 7 69 Glencoe Geometry
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
NAME DATE PERIOD
7
Part 3: Short Response
Instructions: Write your answers in the spaces provided.
15. Solve -16
− 40
= 4x + 10
− 5 . (Lesson 7-1)
16. −−
XA is an altitude of △XYB. Find the value of y. (Lesson 5-2)
17. Two sides of a triangle measure 21 inches and 32 inches, and the third side measures x inches. Find the range for the value of x. (Lesson 5-5)
18. If △ABC ∼ △HIJ, find the perimeter of △HIJ. (Lesson 7-2)
19. Given T(3, -1), U(1, -7), V(8, -5), W(2, 6), X(-4, 8), and Y(-2, 1), determine whether △TUV $ △WXY. Explain. (Lesson 4-4)
20. Two parallel lines are cut by a transversal, ∠1 and ∠2 are adjacent angles, m∠1 = 12y + 10, and m∠2 = 20y - 34. Find m∠1 and m∠2. (Lesson 3-2)
21. Use points S(-5, 7), T(1, 9), P(12, -1), and R(3, 26).
a. Find the lengths of −−
ST and −−
PR to the nearest hundredth. (Lesson 1-3)
b. Determine the slope of −−
ST and of −−
PR . (Lesson 3-3)
c. Are −−
ST and −−
PR parallel, perpendicular, or neither? (Lesson 3-3)
32 cm
80 cm
60 cm
A B
C12 cm
H I
J
(2y - 81)°B
A
X
Y
15.
16.
17.
18.
19.
20
21a.
21b.
21c.
Standardized Test Practice (continued)
Chapter 7 70 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-1
Ch
ap
ter
7
5
Gle
nc
oe
Ge
om
etr
y
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Rati
os a
nd
Pro
po
rtio
ns
Wri
te a
nd
Use
Ra
tio
s A
ra
tio
is
a c
om
pari
son
of
two q
uan
titi
es
by d
ivis
ion
s. T
he
rati
o a
to b
, w
here
b i
s n
ot
zero
, ca
n b
e w
ritt
en
as
a
−
b o
r a
:b.
In
20
07
th
e B
osto
n R
ed
So
x b
ase
ba
ll t
ea
m w
on
96
ga
me
s o
ut
of
16
2
ga
me
s p
lay
ed
. W
rit
e a
ra
tio
fo
r t
he
nu
mb
er o
f g
am
es w
on
to
th
e t
ota
l n
um
be
r o
f
ga
me
s p
lay
ed
.
To f
ind
th
e r
ati
o,
div
ide t
he n
um
ber
of
gam
es
won
by t
he t
ota
l n
um
ber
of
gam
es
pla
yed
. T
he
resu
lt i
s 9
6
−
162 ,
wh
ich
is
abou
t 0.5
9.
Th
e B
ost
on
Red
Sox w
on
abou
t 59%
of
their
gam
es
in
2007.
Th
e r
ati
o o
f th
e m
ea
su
re
s o
f th
e a
ng
les
in △
JH
K i
s 2
:3:4
. F
ind
th
e m
ea
su
re
s o
f th
e a
ng
les.
Th
e e
xte
nd
ed
rati
o 2
:3:4
can
be r
ew
ritt
en
2x:3
x:4
x.
Sk
etc
h a
nd
label
the a
ngle
measu
res
of
the t
rian
gle
. T
hen
wri
te a
nd
solv
e a
n e
qu
ati
on
to f
ind
th
e v
alu
e o
f x.
2x +
3x +
4x =
180
Triangle
Sum
Theore
m
9x =
180
Com
bin
e lik
e t
erm
s.
x =
20
Div
ide e
ach s
ide b
y 9
.
Th
e m
easu
res
of
the a
ngle
s are
2(2
0)
or
40,
3(2
0)
or
60,
an
d 4
(20)
or
80.
Exerc
ises
1
. In
th
e 2
007 M
ajo
r L
eagu
e B
ase
ball
seaso
n,
Ale
x R
od
rigu
ez h
it 5
4 h
om
e r
un
s an
d w
as
at
bat
583 t
imes.
Wh
at
is t
he r
ati
o o
f h
om
e r
un
s to
th
e n
um
ber
of
tim
es
he w
as
at
bat?
5
4
−
58
3 o
r ab
ou
t 0.0
926
2. T
here
are
182 g
irls
in
th
e s
op
hom
ore
cla
ss o
f 305 s
tud
en
ts.
Wh
at
is t
he r
ati
o o
f gir
ls t
o
tota
l st
ud
en
ts?
1
82
−
30
5
3. T
he l
en
gth
of
a r
ect
an
gle
is
8 i
nch
es
an
d i
ts w
idth
is
5 i
nch
es.
Wh
at
is t
he r
ati
o o
f le
ngth
to w
idth
?
8
−
5
4. T
he
rati
o of
th
e si
des
of
a t
rian
gle
is
8:1
5:1
7. It
s peri
mete
r is
480 i
nch
es. F
ind t
he l
en
gth
of
each
sid
e of
th
e tr
ian
gle
.
96 i
n., 1
80 i
n., 2
04 i
n.
5. T
he
rati
o of
th
e m
easu
res
of t
he t
hre
e a
ngle
s of
a t
rian
gle
is
7:9
:20. F
ind t
he m
easu
re o
f each
an
gle
of
the
tria
ngle
.
35, 45, 100
Exam
ple
1
Exam
ple
2
7-1
4x°
2x°
3x°
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
3
Gle
nc
oe
Ge
om
etr
y
An
tici
pati
on
Gu
ide
Pro
po
rtio
ns a
nd
Sim
ilari
ty
7
B
efo
re y
ou
beg
in C
ha
pte
r 7
•
R
ead
each
sta
tem
en
t.
•
D
eci
de w
heth
er
you
Agre
e (
A)
or
Dis
agre
e (
D)
wit
h t
he s
tate
men
t.
•
W
rite
A o
r D
in
th
e f
irst
colu
mn
OR
if
you
are
not
sure
wh
eth
er
you
agre
e o
r d
isagre
e,
wri
te N
S (
Not
Su
re).
A
fter y
ou
co
mp
lete
Ch
ap
ter 7
•
R
ere
ad
each
sta
tem
en
t an
d c
om
ple
te t
he l
ast
colu
mn
by e
nte
rin
g a
n A
or
a D
.
•
D
id a
ny o
f you
r op
inio
ns
abou
t th
e s
tate
men
ts c
han
ge f
rom
th
e f
irst
colu
mn
?
•
F
or
those
sta
tem
en
ts t
hat
you
mark
wit
h a
D,
use
a p
iece
of
pap
er
to w
rite
an
exam
ple
of
wh
y y
ou
dis
agre
e.
Ste
p 2
Ste
p 1
ST
EP
1A
, D
, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1
. R
ati
os
are
alw
ays
wri
tten
as
fract
ion
s.
2
. A
pro
port
ion
is
an
equ
ati
on
sta
tin
g t
hat
two r
ati
os
are
equ
al.
3
. T
wo r
ati
os
are
in
pro
port
ion
to e
ach
oth
er
on
ly i
f th
eir
cr
oss
pro
du
cts
are
equ
al.
4
. If
a
−
b =
c
−
d , t
hen
ad
= b
c.
5
. T
he r
ati
o o
f th
e l
en
gth
s of
the s
ides
of
sim
ilar
figu
res
is
call
ed
th
e s
cale
fact
or
for
the t
wo f
igu
res.
6
. If
on
e a
ngle
in
a t
rian
gle
is
con
gru
en
t to
an
an
gle
in
an
oth
er
tria
ngle
, th
en
th
e t
wo t
rian
gle
s are
sim
ilar.
7
. If
a l
ine i
s p
ara
llel
to o
ne s
ide o
f a t
rian
gle
an
d i
nte
rsect
s th
e o
ther
two s
ides
in t
wo d
isti
nct
poin
ts,
then
th
e l
ine
sep
ara
tes
the t
wo s
ides
into
con
gru
en
t se
gm
en
ts.
8
. A
segm
en
t w
hose
en
dp
oin
ts a
re t
he m
idp
oin
ts o
f tw
o
sid
es
of
a t
rian
gle
is
para
llel
to t
he t
hir
d s
ide o
f th
e
tria
ngle
.
9
. If
tw
o t
rian
gle
s are
sim
ilar
then
th
eir
peri
mete
rs a
re
equ
al.
10
. T
he m
ed
ian
s of
two s
imil
ar
tria
ngle
s are
in
th
e s
am
e
pro
port
ion
as
corr
esp
on
din
g s
ides.
D A A D A D D A D A
Answers (Anticipation Guide and Lesson 7-1)
Chapter 7 A1 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Answers (Lesson 7-1)
Chapter 7 A2 Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
6
Gle
nc
oe
Ge
om
etr
y
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Rati
os a
nd
Pro
po
rtio
ns
Use
Pro
pe
rtie
s o
f P
rop
ort
ion
s A
sta
tem
ent
that
two
rati
os a
re
equ
al
is c
all
ed a
pro
po
rti
on
. In
th
e p
rop
orti
on a
−
b =
c −
d ,
wh
ere
b a
nd
d a
re
not
zer
o, t
he
valu
es a
an
d d
are
th
e e
xtr
em
es a
nd
th
e valu
es b
an
d c
are
th
e m
ea
ns.
In a
pro
por
tion
, th
e p
rod
uct
of
the
mea
ns
is e
qu
al
to t
he
pro
du
ct o
f th
e ex
trem
es,
so a
d =
bc.
Th
is i
s th
e C
ross
Pro
du
ct P
rop
erty
.
S
olv
e
9
−
16 =
27
−
x .
9
−
16 =
27
−
x
9 ·
x =
16
· 2
7
Cro
ss P
roducts
Pro
pert
y
9x =
432
Multip
ly.
x =
48
D
ivid
e e
ach s
ide b
y 9
.
PO
LIT
ICS
Ma
yo
r H
ern
an
de
z c
on
du
cte
d a
ra
nd
om
su
rv
ey
of
20
0 v
ote
rs a
nd
fo
un
d t
ha
t 1
35
ap
pro
ve
of
the
jo
b s
he
is d
oin
g.
If t
he
re
are
48
,00
0 v
ote
rs i
n M
ay
or H
ern
an
de
z’s
to
wn
, p
re
dic
t th
e t
ota
l n
um
be
r o
f v
ote
rs
wh
o a
pp
ro
ve
of
the
jo
b s
he
is d
oin
g.
Wri
te a
nd
sol
ve
a p
rop
orti
on t
hat
com
pare
s th
e n
um
ber
of
regis
tere
d v
oter
s an
d t
he
nu
mber
of
reg
iste
red
vot
ers
wh
o ap
pro
ve
of t
he
job t
he
mayor
is
doi
ng.
1
35
−
200 =
x
−
48,0
00
← v
ote
rs w
ho a
ppro
ve
← a
ll vote
rs
135 ·
48,0
00 =
20
0 ·
x
Cro
ss P
roducts
Pro
pert
y
6,4
80,0
00 =
20
0x
Sim
plif
y.
32,4
00 =
x
Div
ide e
ach s
ide b
y 2
00.
Base
d o
n t
he
surv
ey,
abou
t 32,4
00 r
egis
tere
d v
oter
s ap
pro
ve
of t
he
job t
he
mayor
is
doi
ng.
Exerc
ises
So
lve
ea
ch
pro
po
rti
on
.
1.
1
−
2 =
28
−
x
56
2.
3
−
8 =
y
−
24 9
3.
x +
22
−
x +
2
= 3
0
−
10 8
4.
3
−
18.2
= 9
−
y 54.6
5. 2
x +
3
−
8
=
5
−
4 3.5
6. x
+ 1
−
x -
1
= 3
−
4
-7
7. If
3 D
VD
s co
st $
44.8
5,
fin
d t
he
cost
of
one
DV
D.
$14.9
5
8
. B
OT
AN
Y B
ryon
is
mea
suri
ng p
lan
ts i
n a
fie
ld f
or a
sci
ence
pro
ject
. O
f th
e fi
rst
25
pla
nts
he
mea
sure
s, 1
5 o
f th
em a
re s
mall
er t
han
a f
oot
in h
eigh
t. I
f th
ere
are
4000
pla
nts
in
th
e fi
eld
, p
red
ict
the
tota
l n
um
ber
of
pla
nts
sm
all
er t
han
a f
oot
in h
eigh
t.
2
400 p
lan
ts
7-1
Exam
ple
1
Exam
ple
2
a
−
b =
c −
d
a ·
d =
b ·
c
extr
em
es
means
↑↑
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-1
Ch
ap
ter
7
7
Gle
nc
oe
Ge
om
etr
y
Sk
ills
Pra
ctic
e
Rati
os a
nd
Pro
po
rtio
ns
7-1
1. FO
OT
BA
LL A
tig
ht
end
sco
red
6 t
ouch
dow
ns
in 1
4 g
am
es.
Fin
d t
he
rati
o of
tou
chd
own
s p
er g
am
e.
0.4
3:1
2. E
DU
CA
TIO
N I
n a
sch
edu
le o
f 6 c
lass
es,
Mart
a h
as
2 e
lect
ive
class
es.
Wh
at
is t
he
rati
o of
ele
ctiv
e to
non
-ele
ctiv
e cl
ass
es i
n M
art
a’s
sch
edu
le?
1:2
3. B
IOLO
GY
Ou
t of
274 l
iste
d s
pec
ies
of b
ird
s in
th
e U
nit
ed S
tate
s, 7
8 s
pec
ies
mad
e th
e en
dan
ger
ed l
ist.
Fin
d t
he
rati
o of
en
dan
ger
ed s
pec
ies
of b
ird
s to
lis
ted
sp
ecie
s in
th
e U
nit
ed S
tate
s.
39:1
37
4. B
OA
RD
GA
ME
S M
yra
is
pla
yin
g a
boa
rd g
am
e. A
fter
12 t
urn
s, M
yra
has
lan
ded
on
a
blu
e sp
ace
3 t
imes
. If
th
e gam
e w
ill
last
for
100 t
urn
s, p
red
ict
how
man
y t
imes
Myra
w
ill
lan
d o
n a
blu
e sp
ace
.
25
5. S
CH
OO
L T
he
rati
o of
male
stu
den
ts t
o fe
male
stu
den
ts i
n t
he
dra
ma c
lub a
t C
am
pbel
l H
igh
Sch
ool
is 3
:4.
If t
he
nu
mber
of
male
stu
den
ts i
n t
he
clu
b i
s 18,
pre
dic
t th
e n
um
ber
of
fem
ale
stu
den
ts?
24
So
lve
ea
ch
pro
po
rti
on
.
6
. 2
−
5 =
x
−
40
16
7
.
7
−
10 =
21
−
x
30
8
. 2
0
−
5
= 4
x
−
6
6
9
. 5
x
−
4
= 3
5
−
8
3.5
1
0. x
+1
−
3
= 7
−
2
9.5
1
1.
15
−
3
= x
-3
−
5
28
12
. Th
e ra
tio
of t
he
mea
sure
s of
th
e si
des
of
a t
rian
gle
is
3:5
:7,
an
d i
ts p
erim
eter
is
450 c
enti
met
ers.
Fin
d t
he
mea
sure
s of
each
sid
e of
th
e tr
ian
gle
.
90 c
m,
150 c
m,
210 c
m
13
. Th
e ra
tio
of t
he
mea
sure
s of
th
e si
des
of
a t
rian
gle
is
5:6
:9, an
d i
ts p
erim
eter
is
220 m
eter
s.
Wh
at
are
th
e m
easu
res
of t
he
sid
es o
f th
e tr
ian
gle
?
55 m
, 66 m
, 99 m
14
. Th
e ra
tio
of t
he
mea
sure
s of
th
e si
des
of
a t
rian
gle
is
4:6
:8,
an
d i
ts p
erim
eter
is
126 f
eet.
W
hat
are
th
e m
easu
res
of t
he
sid
es o
f th
e tr
ian
gle
?
28 f
t, 4
2 f
t, 5
6 f
t
15
. Th
e ra
tio
of t
he
mea
sure
s of
th
e si
des
of
a t
rian
gle
is
5:7
:8,
an
d i
ts p
erim
eter
is
40 i
nch
es.
Fin
d t
he
mea
sure
s of
each
sid
e of
th
e tr
ian
gle
.
10 i
n., 1
4 i
n., 1
6 i
n.
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Answers (Lesson 7-1)
Chapter 7 A3 Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
8
Gle
nc
oe
Ge
om
etr
y
Practi
ce
Rati
os a
nd
Pro
po
rtio
ns
1. N
UT
RIT
ION
O
ne o
un
ce o
f ch
ed
dar
cheese
con
tain
s 9 g
ram
s of
fat.
Six
of
the g
ram
s of
fat
are
satu
rate
d f
ats
. F
ind
th
e r
ati
o o
f sa
tura
ted
fats
to t
ota
l fa
t in
an
ou
nce
of
cheese
.
2
. FA
RM
ING
T
he r
ati
o o
f goats
to s
heep
at
a u
niv
ers
ity r
ese
arc
h f
arm
is
4:7
. T
he n
um
ber
of
sheep
at
the f
arm
is
28.
Wh
at
is t
he n
um
ber
of
goats
?
3
. Q
UA
LIT
Y C
ON
TR
OL
A w
ork
er
at
an
au
tom
obil
e a
ssem
bly
pla
nt
check
s n
ew
cars
for
defe
cts.
Of
the f
irst
280 c
ars
he c
heck
s, 4
have d
efe
cts.
If
10,5
00 c
ars
wil
l be c
heck
ed
th
is
mon
th,
pre
dic
t th
e t
ota
l n
um
ber
of
cars
th
at
wil
l h
ave d
efe
cts.
150 c
ars
So
lve
ea
ch
pro
po
rti
on
.
4.
5
−
8 =
x
−
12
5.
x
−
1.1
2 =
1
−
5
6.
6x
−
27 =
43
7.
x +
2
−
3
= 8
−
9
2
−
3
8.
3x -
5
−
4
= -
5
−
7
5
−
7
9.
x -
2
−
4
= x
+ 4
−
2
10. T
he r
ati
o o
f th
e m
easu
res
of
the s
ides
of
a t
rian
gle
is
3:4
:6,
an
d i
ts p
eri
mete
r is
104 f
eet.
Fin
d t
he m
easu
re o
f each
sid
e o
f th
e t
rian
gle
.
11. T
he r
ati
o o
f th
e m
easu
res
of
the s
ides
of
a t
rian
gle
is
7:9
:12,
an
d i
ts p
eri
mete
r is
84 i
nch
es.
Fin
d t
he m
easu
re o
f each
sid
e o
f th
e t
rian
gle
.
12. T
he r
ati
o o
f th
e m
easu
res
of
the s
ides
of
a t
rian
gle
is
6:7
:9,
an
d i
ts p
eri
mete
r is
77 c
en
tim
ete
rs.
Fin
d t
he m
easu
re o
f each
sid
e o
f th
e t
rian
gle
.
13. T
he r
ati
o o
f th
e m
easu
res
of
the t
hre
e a
ngle
s is
4:5
:6.
Fin
d t
he m
easu
re o
f each
an
gle
of
the t
rian
gle
.
14. T
he r
ati
o o
f th
e m
easu
res
of
the t
hre
e a
ngle
s is
5:7
:8.
Fin
d t
he m
easu
re o
f each
an
gle
of
the t
rian
gle
.
15. B
RID
GE
S A
con
stru
ctio
n w
ork
er
is p
laci
ng r
ivets
in
a n
ew
bri
dge. H
e u
ses
42 r
ivets
to b
uil
d
the f
irst
2 f
eet
of
the b
ridge. If
th
e b
ridge i
s to
be 2
200 f
eet
in l
en
gth
, pre
dic
t th
e n
um
ber
of
rivets
th
at
wil
l be n
eeded f
or
the e
nti
re b
ridge.
4
6,2
00 r
ivets
7-1 2
:3
16
7.5
0.2
24
193.5 -
10
24 f
t, 3
2 f
t, 4
8 f
t
21 i
n., 2
7 i
n., 3
6 i
n.
21 c
m,
24.5
cm
, 31.5
cm
48,
60,
72
45,
63,
72
Lesson 7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
9
Gle
nc
oe
Ge
om
etr
y
Wo
rd
Pro
ble
m P
racti
ce
Rati
os a
nd
Pro
po
rtio
ns
1
. T
RIA
NG
LE
ST
he r
ati
os
of
the m
easu
res
of
the a
ngle
s in
△D
EF
is 7
:13:1
6.
13
x°
16
x° 7
x°
Fin
d t
he m
easu
re o
f th
e a
ngle
s.
3
5,65,80
2. R
AT
ION
S S
ixte
en
stu
den
ts w
en
t on
a w
eek
-lon
g h
ikin
g t
rip
. T
hey b
rou
gh
t
wit
h t
hem
320 s
peci
all
y b
ak
ed
, p
rote
in-
rich
, co
ok
ies.
Wh
at
is t
he r
ati
o o
f co
ok
ies
to s
tud
en
ts?
3. C
LO
VE
RS
N
ath
an
iel
is s
earc
hin
g f
or
a f
ou
r-le
af
clover
in a
fie
ld.
He f
ind
s
2 f
ou
r-le
af
clovers
du
rin
g t
he f
irst
12 m
inu
tes
of
his
searc
h.
If N
ath
an
iel
spen
ds
a t
ota
l of
180 m
inu
tes
searc
hin
g
in t
he f
ield
, p
red
ict
the n
um
ber
of
fou
r-
leaf
clovers
Nath
an
iel
wil
l fi
nd
.
30 c
lovers
4.C
AR
S A
car
com
pan
y b
uil
ds
two
vers
ion
s of
on
e o
f it
s m
od
els
—a s
ed
an
an
d a
sta
tion
wagon
. T
he r
ati
o o
f se
dan
s
to s
tati
on
wagon
s is
11:2
. A
fre
igh
ter
begin
s u
nlo
ad
ing t
he c
ars
at
a d
ock
.
Tom
cou
nts
18 s
tati
on
wagon
s an
d t
hen
overh
ears
a d
ock
work
er
call
ou
t, “
Ok
ay,
that’
s all
of
the w
agon
s . . .
bri
ng o
ut
the s
ed
an
s!”
How
man
y s
ed
an
s w
ere
on
the s
hip
?
99
5. D
ISA
ST
ER
RE
AD
INE
SS
Th
e t
ow
n o
f
Oyst
er
Bay i
s co
nd
uct
ing a
su
rvey o
f
80 h
ou
seh
old
s to
see h
ow
pre
pare
d i
ts
citi
zen
s are
for
a n
atu
ral
dis
ast
er.
Of
those
hou
seh
old
s su
rveyed
, 66 h
ave a
surv
ival
kit
at
hom
e.
a.
Wri
te t
he r
ati
o o
f p
eop
le w
ith
surv
ival
kit
s in
th
e s
urv
ey.
33
−
40 o
r 0.8
25
b.
Wri
te t
he r
ati
o o
f p
eop
le w
ith
ou
t
surv
ival
kit
s in
th
e s
urv
ey.
7
−
40 o
r 0.1
75
c.
Th
ere
are
29,0
00 h
ou
seh
old
s in
Oyst
er
Bay.
If t
he t
ow
n w
ish
es
to
pu
rch
ase
su
rviv
al
kit
s fo
r all
hou
seh
old
s th
at
do n
ot
curr
en
tly h
ave
on
e,
pre
dic
t th
e n
um
ber
of
kit
s it
wil
l
have t
o p
urc
hase
.
ab
ou
t 5075 k
its
7-1 2
0:1
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
10
G
len
co
e G
eo
me
try
En
rich
men
t
Gro
wth
Ch
art
sIt
is
said
th
at
wh
en
a c
hil
d h
as
reach
ed
th
e a
ge o
f 2 y
ears
, h
e i
s ro
ugh
ly h
alf
of
his
ad
ult
heig
ht.
Th
e g
row
th c
hart
belo
w s
how
s th
e g
row
th a
ccord
ing t
o p
erc
en
tile
s fo
r boys.
1
. U
se t
he c
hart
to d
ete
rmin
e t
he a
pp
roxim
ate
heig
ht
for
a b
oy a
t age 2
if
he i
s in
th
e 7
5th
to 9
5th
perc
en
tile
.
3
5–37 i
nch
es
2
. U
sin
g t
he r
ule
th
at
the h
eig
ht
at
age 2
is
ap
pro
xim
ate
ly h
alf
of
his
ad
ult
heig
ht,
set
up
a
pro
port
ion
to s
olv
e f
or
the a
du
lt h
eig
ht
of
the b
oy i
n E
xerc
ise 1
. S
olv
e y
ou
r p
rop
ort
ion
.
36
−
x
= 1
−
2 ;
72 i
nch
es
3
. U
se t
he c
hart
to a
pp
roxim
ate
th
e h
eig
ht
at
age 1
8 f
or
a b
oy i
f h
e i
s in
th
e 7
5th
to 9
5th
perc
en
tile
. H
ow
does
this
an
swer
com
pare
to t
he a
nsw
er
to p
roble
m 1
?
7
2–74 i
nch
es:
the t
wo
an
sw
ers
are
very
clo
se
4
. R
ep
eat
this
pro
cess
for
a b
oy w
ho i
s in
th
e 5
th t
o 2
5th
perc
en
tile
.
3
2–34 i
nch
es;
66 i
nch
es;
65–68 i
nch
es
5
. Is
usi
ng t
he r
ule
th
at
a b
oy i
s h
alf
of
his
ad
ult
heig
ht
at
age 2
years
a g
ood
ap
pro
xim
ati
on
? E
xp
lain
.
Y
es,
it a
pp
ears
to
be a
go
od
ap
pro
xim
ati
on
.
7-1
85
75
65
55
45
35
24
68
10
12
14
16
18
Ag
e (
yr)
Height (in.)
Perc
en
tile
Gro
up
5th
to
25th
25th
to
75th
75th
to
95th
A
B
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-1
Ch
ap
ter
7
11
G
len
co
e G
eo
me
try
You
can
use
a c
alc
ula
tor
to s
olv
e p
rop
ort
ion
s.
S
olv
e t
he
pro
po
rti
on
by
usin
g c
ro
ss p
ro
du
cts
. R
ou
nd
yo
ur a
nsw
er
to t
he
ne
are
st
hu
nd
re
dth
.
55.6
−
16.9
= 4
5.8
−
x
Mu
ltip
ly 1
6.9
by 4
5.8
. D
ivid
e t
he p
rod
uct
by 5
5.6
.
En
ter:
16.9
3
45.8
÷
55.6
E
NT
ER
13.92122302
Th
e s
olu
tion
is
ap
pro
xim
ate
ly 1
3.9
2
So
lve
ea
ch
pro
po
rti
on
by
usin
g c
ro
ss p
ro
du
cts
. R
ou
nd
yo
ur a
nsw
ers
to t
he
ne
are
st
hu
nd
re
dth
.
1
. 1
3.9
−
39.8
=
10.5
−
x
2
. 2
5.9
−
37.7
=
24.3
−
x
3
. 1
9.6
−
54.3
=
27.7
−
x
4
. 6
6.8
−
43.4
=
x
−
16.9
5
. 7
5.4
−
37.2
=
x
−
32.4
6
.
x
−
46.2
=
29.7
−
36.4
7
.
x
−
14.9
=
16.8
−
24.6
8
. 3
5.8
−
x
=
32.9
−
27.8
9
. 4
6.9
−
x
=
15.7
−
99.9
10
. 3
4.9
−
21.1
=
x
−
36.6
1
1.
x
−
99.8
=
32.2
−
45.3
1
2. 6
8.9
−
x
=
44.3
−
86.4
x ≈
30.0
6
x ≈
35.3
7
x ≈
76.7
4
7-1
Gra
ph
ing C
alc
ula
tor
Act
ivit
y
So
lvin
g P
rop
ort
ion
s
Exam
ple
x ≈
26.0
1
x ≈
65.6
7
x ≈
37.7
0
x ≈
10.1
8
x ≈
30.2
5
x ≈
298.4
3
x ≈
60.5
4
x ≈
70.9
4
x ≈
134.3
8
Answers (Lesson 7-1)
Chapter 7 A4 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
12
G
len
co
e G
eo
me
try
Ide
nti
fy S
imil
ar
Po
lyg
on
s S
imil
ar
poly
gon
s h
ave t
he s
am
e s
hap
e b
ut
not
nece
ssari
ly
the s
am
e s
ize.
If △
AB
C ∼
△X
YZ
, li
st
all
pa
irs o
f co
ng
ru
en
t a
ng
les a
nd
writ
e a
pro
po
rti
on
th
at
re
late
s t
he
co
rre
sp
on
din
g s
ide
s.
Use
th
e s
imil
ari
ty s
tate
men
t.
Con
gru
en
t an
gle
s: ∠
A !
∠X
, ∠
B !
∠Y
, ∠
C !
∠Z
Pro
port
ion
: A
B
−
XY
= B
C
−
YZ
= C
A
−
ZX
De
term
ine
wh
eth
er t
he
pa
ir o
f fi
gu
re
s i
s s
imil
ar.
If s
o,
writ
e t
he
sim
ila
rit
y s
tate
me
nt
an
d s
ca
le f
acto
r.
Ex
pla
in y
ou
r r
ea
so
nin
g.
Ste
p 1
C
om
pare
corr
esp
on
din
g a
ngle
s.∠
W !
∠P
, ∠
X !
∠Q
, ∠
Y !
∠R
, ∠
Z !
∠S
Corr
esp
on
din
g a
ngle
s are
con
gru
en
t.
Ste
p 2
C
om
pare
corr
esp
on
din
g s
ides.
WX
−
PQ
=
12
−
8
= 3
−
2 ,
XY
−
QR
= 1
8
−
12 =
3
−
2 ,
YZ
−
RS
= 1
5
−
10 =
3
−
2 ,
an
d
Z
W
−
SP
=
9
−
6 =
3
−
2 .
Sin
ce c
orr
esp
on
din
g s
ides
are
pro
port
ion
al,
WX
YZ
∼ P
QR
S.
Th
e p
oly
gon
s are
sim
ilar
wit
h a
sca
le f
act
or
of
3
−
2 .
Exerc
ises
Lis
t a
ll p
air
s o
f co
ng
ru
en
t a
ng
les,
an
d w
rit
e a
pro
po
rti
on
th
at
re
late
s t
he
co
rre
sp
on
din
g s
ide
s
for e
ach
pa
ir o
f sim
ila
r p
oly
go
ns.
1
. △
DE
F ∼
△G
HJ
∠D
# ∠
G,
∠E
# ∠
J,
∠F #
∠H
; D
E
−
GJ =
EF
−
HJ =
FD
−
HG
2
. P
QR
S ∼
TU
WX
∠P
# ∠
T,
∠Q
# ∠
U,
∠R
# ∠
W,
∠S
# ∠
X;
PQ
−
TU
=
QR
−
UW
= R
S
−
WX =
SP
−
XT
De
term
ine
wh
eth
er e
ach
pa
ir o
f fi
gu
re
s i
s s
imil
ar.
If s
o,
writ
e t
he
sim
ila
rit
y
sta
tem
en
t a
nd
sca
le f
acto
r.
If n
ot,
ex
pla
in y
ou
r r
ea
so
nin
g.
3
.
4.
22
11
7-2
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sim
ilar
Po
lyg
on
s
Exam
ple
1
15
9
12
18
XW
ZY
10
6
8
12
QP S
R
Exam
ple
2
no
, ∠
L ≇
∠E
△P
QR
∼ △
PS
T;
scale
facto
r 1
−
2
Lesson 7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
13
G
len
co
e G
eo
me
try
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Sim
ilar
Po
lyg
on
s
Use
Sim
ila
r Fig
ure
s Y
ou
can
use
sca
le f
act
ors
an
d p
rop
ort
ion
s to
fin
d m
issi
ng s
ide
len
gth
s in
sim
ilar
poly
gon
s.
Th
e t
wo
po
lyg
on
s a
re
sim
ila
r.
Fin
d x
an
d y
.
x
y38
32
16
13
T
S
RP
N
M
Use
th
e c
on
gru
en
t an
gle
s to
wri
te t
he
corr
esp
on
din
g v
ert
ices
in o
rder.
△R
ST
∼ △
MN
P
Wri
te p
rop
ort
ion
s to
fin
d x
an
d y
.
3
2
−
16 =
x
−
13
38
−
y
= 3
2
−
16
16x =
32(1
3)
32y =
38(1
6)
x =
26
y =
19
If
△D
EF
∼ △
GH
J,
fin
d t
he
sca
le f
acto
r o
f △
DE
F t
o △
GH
J a
nd
th
e
pe
rim
ete
r o
f e
ach
tria
ng
le.
Th
e s
cale
fact
or
is
E
F
−
HJ =
8
−
12 =
2
−
3 .
Th
e p
eri
mete
r of
△D
EF
is
10 +
8 +
12 o
r 30.
2
−
3 =
Peri
mete
r of
△D
EF
−
−
P
eri
mete
r of
△G
HJ
Theore
m 7
.1
2
−
3 =
30
−
x
Substitu
tion
(3)(
30)
= 2
x
Cro
ss P
roducts
Pro
pert
y
45
= x
S
olv
e.
So,
the p
eri
mete
r of
△G
HJ
is
45.
Exerc
ises
Ea
ch
pa
ir o
f p
oly
go
ns i
s s
imil
ar.
Fin
d t
he
va
lue
of
x.
1.
9
12
8 10
x
2.
10
4.5
x
2.5 5
3.
12
x+
1
18
24
18
4.
40
36
x+
15
30
18
5. If
AB
CD
∼ P
QR
S, fi
nd t
he s
cale
fact
or
of A
BC
D t
o P
QR
S a
nd t
he
peri
mete
r
of e
ach
pol
ygon
.
s
cale
facto
r 4
−
5 ;
peri
mete
r A
BC
D =
68;
p
eri
mete
r P
QR
S =
85;
7-2
Exam
ple
1Exam
ple
2
12
12
10
8
14
20
25
x
= 6
x
= 2
.25
x =
15
x =
9
Answers (Lesson 7-2)
Chapter 7 A5 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
14
G
len
co
e G
eo
me
try
De
term
ine
wh
eth
er e
ach
pa
ir o
f fi
gu
re
s i
s s
imil
ar.
If s
o,
writ
e t
he
sim
ila
rit
y
sta
tem
en
t a
nd
sca
le f
acto
r.
If n
ot,
ex
pla
in y
ou
r r
ea
so
nin
g.
1
.
2.
7.5
7.5
7.5
7.5
ZY
XW
3
3
33
SR
QP
Ea
ch
pa
ir o
f p
oly
go
ns i
s s
imil
ar.
Fin
d t
he
va
lue
of x
.
3
.
4
.
5
.
6
.
9
10 3
x+
1
5
P
S
R
UV
WT
Q
10
8
x+
2
x-
1
SP
MN
L
T
x+
5
x+
5
9
3
44
S
W
XY
T U26
14
12
13
BC
DA
13
7
6x G
EH
F
10.5
69
59°
35°
AC
B
7
46
59°
35°
DF
E
△A
BC
∼ △
DE
F;
∠A
# ∠
D,
rh
om
bu
s P
QR
S ∼
rh
om
bu
s W
XY
Z;
∠C
# ∠
F,
an
d ∠
B #
∠E
∠P
# ∠
W,
∠Q
# ∠
X,
∠R
# ∠
Y,
by t
he T
hir
d A
ng
le T
heo
rem
, an
d
∠
S #
∠Z
; P
Q
−
WX
=
QR
−
XY =
R
S
−
YZ
=
SP
−
ZW
;
A
B
−
DE
=
BC
−
EF =
C
A
−
FD
; scale
facto
r: 3
−
2 .
scale
facto
r:
3
−
7.5
=
0.4
6
.5
7
5
13
Sk
ills
Practi
ce
Sim
ilar
Po
lyg
on
s
7-2
Lesson 7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
15
G
len
co
e G
eo
me
try
Practi
ce
Sim
ilar
Po
lyg
on
sD
ete
rm
ine
wh
eth
er e
ach
pa
ir o
f fi
gu
re
s i
s s
imil
ar.
If s
o,
writ
e t
he
sim
ila
rit
y
sta
tem
en
t a
nd
sca
le f
acto
r.
If n
ot,
ex
pla
in y
ou
r r
ea
so
nin
g.
1.
25
12
9
14
.4
15
24
20
15
JM
QRS
PK
L
2.
24
12
14
16
21
18
VU
AC
BT
Ea
ch
pa
ir o
f p
oly
go
ns i
s s
imil
ar.
Fin
d t
he
va
lue
of x.
3.
14
10
x+
6
x+
9
CN
MD
AB
LP
4.
61
2
40°
40°
x+
1
x-
3A
F
E
D
BC
5
. P
EN
TA
GO
NS
If
AB
CD
E ∼
PQ
RS
T,
fin
d t
he
scale
fact
or
of
AB
CD
E t
o P
QR
ST
an
d t
he
peri
mete
r of
each
poly
gon
.
6. S
WIM
MIN
G P
OO
LS
T
he M
inn
itte
fam
ily
an
d t
he n
eig
hbori
ng G
au
det
fam
ily b
oth
have i
n-g
rou
nd
sw
imm
ing p
ools
. T
he
Min
nit
te f
am
ily p
ool,
PQ
RS
, m
easu
res
48 f
eet
by 8
4 f
eet.
Th
e G
au
det
fam
ily p
ool,
WX
YZ
, m
easu
res
40 f
eet
by 7
0 f
eet.
Are
the t
wo p
ools
sim
ilar?
If
so,
wri
te t
he
sim
ilari
ty s
tate
men
t an
d s
cale
fact
or.
7-2
20
15
10
21
48 ft
84 ft
70 ft
40 ft
P Q
SW Z
X Y
R
3
−
2
7
J
KLM
∼ Q
RS
P;
△
AB
C ∼
△U
VT;
∠A
# ∠
U,
∠J #
∠Q
, ∠
K #
∠R
,
∠
B #
∠V
, an
d ∠
C #
∠T
by t
he
∠L
# ∠
S,
∠M
# ∠
P,
an
d
Th
ird
An
gle
Th
eo
rem
an
d
JK
−
QR
= K
L
−
RS =
LM
−
SP
= M
J
−
PQ
= 5
−
3 o
r 1.6
7
A
B
−
UV =
BC
−
VT
= C
A
−
TU
= 2
−
3 .
scale
facto
r 5
−
7 ;
peri
mete
r A
BC
DE
= 6
5;
peri
mete
r P
QR
ST =
91
yes;
PQ
RS
∼ W
XY
Z;
scale
facto
r 6
−
5
Answers (Lesson 7-2)
Chapter 7 A6 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
16
G
len
co
e G
eo
me
try
Wo
rd
Pro
ble
m P
racti
ce
Sim
ilar
Po
lyg
on
s
1
. P
AN
ELS
W
hen
clo
sed
, an
en
tert
ain
men
t ce
nte
r is
mad
e o
f fo
ur
squ
are
pan
els
. T
he t
hre
e s
mall
er
pan
els
are
con
gru
en
t sq
uare
s.
Wh
at
is t
he s
cale
fact
or
of
the l
arg
er
squ
are
to o
ne o
f th
e s
mall
er
squ
are
s?
2
. W
IDE
SC
RE
EN
TE
LE
VIS
ION
S A
n
ele
ctro
nic
s co
mp
an
y m
an
ufa
ctu
res
wid
esc
reen
tele
vis
ion
sets
in
severa
l d
iffe
ren
t si
zes.
Th
e r
ect
an
gu
lar
vie
win
g
are
a o
f each
tele
vis
ion
siz
e i
s si
mil
ar
to
the v
iew
ing a
reas
of
the o
ther
sizes.
Th
e
com
pan
y’s
42-i
nch
wid
esc
reen
tele
vis
ion
h
as
a v
iew
ing a
rea p
eri
mete
r of
ap
pro
xim
ate
ly 1
44.4
in
ches.
Wh
at
is t
he
vie
win
g a
rea p
eri
mete
r of
the c
om
pan
y’s
46-i
nch
wid
esc
reen
tele
vis
ion
?
3
. IC
E H
OC
KE
Y A
n o
ffic
ial
Oly
mp
ic-s
ized
ic
e h
ock
ey r
ink
measu
res
30 m
ete
rs b
y
60 m
ete
rs.
Th
e i
ce h
ock
ey r
ink
at
the
loca
l co
mm
un
ity c
oll
ege m
easu
res
25.5
m
ete
rs b
y 5
1 m
ete
rs.
Are
th
e i
ce h
ock
ey
rin
ks
sim
ilar?
Exp
lain
you
r re
aso
nin
g.
4
. E
NLA
RG
ING
C
am
ille
wan
ts t
o m
ak
e
a p
att
ern
for
a f
ou
r-p
oin
ted
sta
r w
ith
d
imen
sion
s tw
ice a
s lo
ng a
s th
e o
ne
show
n.
Help
her
by d
raw
ing a
sta
r w
ith
dim
en
sion
s tw
ice a
s lo
ng o
n t
he
gri
d b
elo
w.
5
. B
IOLO
GY
A
para
meci
um
is
a s
mall
si
ngle
-cell
org
an
ism
. T
he p
ara
meci
um
m
agn
ifie
d b
elo
w i
s act
uall
y o
ne t
en
th
of
a m
illi
mete
r lo
ng.
a.
If y
ou
wan
t to
mak
e a
ph
oto
gra
ph
of
the o
rigin
al
para
meci
um
so t
hat
its
image i
s 1 c
en
tim
ete
r lo
ng,
by w
hat
scale
fact
or
shou
ld y
ou
magn
ify i
t?
b.
If y
ou
wan
t to
mak
e a
ph
oto
gra
ph
of
the o
rigin
al
para
meci
um
so t
hat
its
image i
s 15 c
en
tim
ete
rs l
on
g,
by w
hat
scale
fact
or
shou
ld y
ou
magn
ify i
t?
c.
By a
pp
roxim
ate
ly w
hat
scale
fact
or
has
the p
ara
meci
um
been
en
larg
ed
to
mak
e t
he i
mage s
how
n?
7-2 3 a
bo
ut
158.2
in
ch
es
100
1500
400
Yes;
the r
ati
o o
f th
e l
on
ger
dim
en
sio
ns o
f th
e r
inks i
s 2
0
−
17
an
d t
he r
ati
o o
f th
e s
maller
dim
en
sio
ns o
f th
e r
inks i
s 2
0
−
17 .
Lesson 7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
17
G
len
co
e G
eo
me
try
En
ric
hm
en
t
Co
nstr
ucti
ng
Sim
ilar
Po
lyg
on
sH
ere
are
fou
r st
ep
s fo
r co
nst
ruct
ing a
poly
gon
th
at
is s
imil
ar
to a
nd
wit
h s
ides
twic
e a
s lo
ng a
s th
ose
of
an
exis
tin
g p
oly
gon
.
Ste
p 1
C
hoose
an
y p
oin
t eit
her
insi
de o
r ou
tsid
e t
he p
oly
gon
an
d l
abel
it O
.
Ste
p 2
D
raw
rays
from
O t
hro
ugh
each
vert
ex o
f th
e p
oly
gon
.
Ste
p 3
F
or
vert
ex V
, se
t th
e c
om
pass
to l
en
gth
OV
. T
hen
loca
te a
new
poin
t V
′ on
ray OV
su
ch t
hat VV
′ =
OV
. T
hu
s, OV
′ =
2(OV
).
Ste
p 4
R
ep
eat
Ste
p 3
for
each
vert
ex.
Con
nect
poin
ts V
′, W
′, X
′ an
d Y
′ to
fo
rm t
he n
ew
poly
gon
.
Tw
o c
on
stru
ctio
ns
of
poly
gon
s si
mil
ar
to a
nd
wit
h s
ides
twic
e t
hose
of VWXY
are
sh
ow
n
belo
w.
Noti
ce t
hat
the p
lace
men
t of
poin
t O
does
not
aff
ect
th
e s
ize o
r sh
ap
e o
f V
′W′X
′Y′,
on
ly i
ts l
oca
tion
.
VW
YX
VW
YX
V'
W'
X'
Y'
O
VW
YX
V'
W'
X'
Y'
O
Tra
ce
ea
ch
po
lyg
on
. T
he
n c
on
str
uct
a s
imil
ar p
oly
go
n w
ith
sid
es t
wic
e a
s l
on
g a
s
tho
se
of
the
giv
en
po
lyg
on
.
1
.
C
A
B
2
. D
EF
G
3
. E
xp
lain
how
to c
on
stru
ct a
sim
ilar
poly
gon
wit
h s
ides
thre
e t
imes
the
len
gth
of
those
of
poly
gon
HIJKL
. T
hen
d
o t
he c
on
stru
ctio
n.
4
. E
xp
lain
how
to c
on
stru
ct a
sim
ilar
poly
gon
1 1
−
2 t
imes
the l
en
gth
of
those
of
poly
gon
MNPQRS
. T
hen
do t
he
con
stru
ctio
n.
7-2
M
S
R
N
Q
P
HI
L
K
J
See s
tud
en
ts’
co
nstr
ucti
on
s.
See s
tud
en
ts’
wo
rk.
See s
tud
en
ts’
wo
rk.
Answers (Lesson 7-2)
Chapter 7 A7 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
18
G
len
co
e G
eo
me
try
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sim
ilar
Tri
an
gle
s
Iden
tify
Sim
ilar
Tri
an
gle
s H
ere
are
th
ree w
ays
to s
how
th
at
two t
rian
gle
s are
sim
ilar.
AA
Sim
ila
rity
Tw
o a
ng
les o
f o
ne
tria
ng
le a
re c
on
gru
en
t to
tw
o a
ng
les o
f a
no
the
r tr
ian
gle
.
SS
S S
imil
ari
tyT
he
me
asu
res o
f th
e c
orr
esp
on
din
g s
ide
le
ng
ths o
f tw
o t
ria
ng
les a
re p
rop
ort
ion
al.
SA
S S
imil
ari
tyT
he
me
asu
res o
f tw
o s
ide
le
ng
ths o
f o
ne
tria
ng
le a
re p
rop
ort
ion
al to
th
e m
ea
su
res o
f tw
o
co
rre
sp
on
din
g s
ide
le
ng
ths o
f a
no
the
r tr
ian
gle
, a
nd
th
e in
clu
de
d a
ng
les a
re c
on
gru
en
t.
D
ete
rm
ine
wh
eth
er t
he
tria
ng
les a
re
sim
ila
r.
15
12
9
DE
F
10
86
AB
C
AC
−
DF
= 6
−
9 =
2
−
3
BC
−
EF
=
8
−
12 =
2
−
3
AB
−
DE
= 1
0
−
15 =
2
−
3
△A
BC
∼ △
DE
F b
y S
SS
Sim
ilari
ty.
D
ete
rm
ine
wh
eth
er t
he
tria
ng
les a
re
sim
ila
r.
8
4
70
°Q
RS
6
3
70
°
M
NP
3
−
4 =
6
−
8 ,
so M
N
−
QR
=
NP
−
RS
.
m∠
N =
m∠
R,
so ∠
N &
∠R
.
△N
MP
∼ △
RQ
S b
y S
AS
Sim
ilari
ty.
Exerc
ises
De
term
ine
wh
eth
er t
he
tria
ng
les a
re
sim
ila
r.
If s
o,
writ
e a
sim
ila
rit
y s
tate
me
nt.
Ex
pla
in y
ou
r r
ea
so
nin
g.
1
.
A
B
C
D
E
F
2
.
36
20
18
24
J
K L
WX
Y
3
. R
S
UL
T
4
.
18
8 65
°9
465
°
D
KJ
P
ZR
5
.
39
26
16
24
F
BE
L
MN
6
. 32
20
15
40
25
24G
H
QR
SI
7-3
Exam
ple
1Exam
ple
2
y
es;
△A
BC
∼ △
DE
F;
AA
Sim
ilari
ty
no
; 3
6
−
24 ≠
20
−
18
y
es;
△R
TU
∼ △
STL;
AA
Sim
ilari
ty
yes;
△K
DJ
∼ △
RP
Z;
SA
S S
imilari
ty
y
es;
△B
FE
∼ △
NLM
; S
AS
Sim
ilari
ty
yes;
△IG
H ∼
△S
QR
; S
SS
Sim
ilari
ty
Lesson 7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
19
G
len
co
e G
eo
me
try
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Sim
ilar
Tri
an
gle
s
Use
Sim
ila
r T
ria
ng
les
Sim
ilar
tria
ngle
s ca
n b
e u
sed
to f
ind
measu
rem
en
ts.
△ABC
∼ △
DEF
. F
ind
th
e
va
lue
s o
f x a
nd
y.
18
√3
B CA
18
18
9
y
x
E FD
A
C
−
DF
= B
C
−
EF
A
B
−
DE
= B
C
−
EF
1
8 √
)
3
−
x
= 1
8
−
9
y
−
18 =
18
−
9
18x =
9(1
8 √
)
3 )
9y =
324
x =
9 √
)
3
y =
36
A
pe
rso
n 6
fe
et
tall
ca
sts
a 1
.5-f
oo
t-lo
ng
sh
ad
ow
at
the
sa
me
tim
e
tha
t a
fla
gp
ole
ca
sts
a 7
-fo
ot-
lon
g
sh
ad
ow
. H
ow
ta
ll i
s t
he
fla
gp
ole
?
7 f
t
6 f
t
?
1.5
ft
Th
e s
un
’s r
ays
form
sim
ilar
tria
ngle
s.
Usi
ng x
for
the h
eig
ht
of
the p
ole
, 6
−
x =
1.5
−
7 ,
so 1
.5x =
42 a
nd
x =
28
.
Th
e f
lagp
ole
is
28 f
eet
tall
.
Exerc
ises
ALG
EB
RA
Id
en
tify
th
e s
imil
ar t
ria
ng
les.
Th
en
fin
d e
ach
me
asu
re
.
1
. J
L
2. IU
3
. Q
R
4. B
C
5
. L
M
6. Q
P
7
. T
he h
eig
hts
of
two v
ert
ical
post
s are
2 m
ete
rs a
nd
0.4
5 m
ete
r. W
hen
th
e s
hort
er
post
ca
sts
a s
had
ow
th
at
is 0
.85 m
ete
r lo
ng,
wh
at
is t
he l
en
gth
of
the l
on
ger
post
’s s
had
ow
to
th
e n
eare
st h
un
dre
dth
?
x3
2
10
22
30
PQ
N
R
F
x
9
87.2
16
K
VP
M
L
24
36
√2
x
36
36
QV
R
S
T
35
13
10
20
JLK
Y
XZ
x
x
60
38
.6
23
30
E
BA
CD
20 13
26
I UW
G
H
x
7-3
Exam
ple
1Exam
ple
2
△
XY
Z ˜
△JK
L;
26
△
GIU
˜ △
GH
W;
30
△
SQ
V ˜
△S
RT;
12
△
BE
D ˜
△B
CA
; 19.3
△
KV
M ˜
△LP
M;
18
△
FR
Q ˜
△FN
P;
10 2
−
3
3.7
8 m
Answers (Lesson 7-3)
Chapter 7 A8 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
NA
ME
DA
TE
PE
RIO
D
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ch
ap
ter
7
20
G
len
co
e G
eo
me
try
De
term
ine
wh
eth
er e
ach
pa
ir o
f tr
ian
gle
s i
s s
imil
ar.
If s
o,
writ
e a
sim
ila
rit
y
sta
tem
en
t. I
f n
ot,
wh
at
wo
uld
be
su
ffic
ien
t to
pro
ve
th
e t
ria
ng
les s
imil
ar? E
xp
lain
yo
ur r
ea
so
nin
g.
1
.
2.
3
.
4.
21
70°
15
MJ
P
14
70°
10
U
S
T
30°
60°
RQM
S
K
T
ALG
EB
RA
Id
en
tify
th
e s
imil
ar t
ria
ng
les.
Th
en
fin
d e
ach
me
asu
re
.
5. AC
6. JL
15
12
D
EC
BAx+
1
x+
5
1
6
4
M
NL
J
K
x+
18
x-
3
7. EH
8. VT
12
9
6
9
D
E
FH G
x+
5
6
14
S
U
V
RT
3x-
3
x+
2
12
12
8
9
96
CP
QR
A
B
Y
es;
△R
ST ∼
△W
SX
(o
r △
XS
W)
Yes;
△A
BC
∼ △
PQ
R (
or
S
AS
Sim
ilari
ty
△Q
PR
) b
y S
SS
Sim
ilari
ty
Y
es;
△S
TU
∼ △
JP
M b
y
Y
es;
△S
KM
∼ △
RTQ
by
S
AS
Sim
ilari
ty
A
A S
imilari
ty
△
AB
C ∼
△D
BE
; 16
△
JK
L ∼
△M
NL;
28
△
DE
F ∼
△G
EH
; 9
△
RS
T ∼
△U
VT;
5.4
Sk
ills
Practi
ce
Sim
ilar
Tri
an
gle
s
7-3
Lesson 7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
21
G
len
co
e G
eo
me
try
Practi
ce
Sim
ilar
Tri
an
gle
s
De
term
ine
wh
eth
er t
he
tria
ng
les a
re
sim
ila
r.
If s
o,
writ
e a
sim
ila
rit
y s
tate
me
nt.
If
no
t, w
ha
t w
ou
ld b
e s
uff
icie
nt
to p
ro
ve
th
e t
ria
ng
les s
imil
ar? E
xp
lain
yo
ur
re
aso
nin
g.
1
.
2.
ALG
EB
RA
Id
en
tify
th
e s
imil
ar t
ria
ng
les.
Th
en
fin
d e
ach
me
asu
re
.
3. LM
, QP
4. NL
, ML
5
.
6.
8
N
JL
K
Mx+
5
6x+
2
24
12
18
N
P
QL
M
x+
3
x-
1
42°
42°
24
18
12
16
J
AK
YS
W
7-3
10
5
12
8
86
x +
7x -
1
x +
1
x +
33
4
7
. IN
DIR
EC
T M
EA
SU
RE
ME
NT
A
lig
hth
ou
se c
ast
s a 1
28-f
oot
shad
ow
. A
nearb
y l
am
pp
ost
that
measu
res
5 f
eet
3 i
nch
es
cast
s an
8-f
oot
shad
ow
.
a.
Wri
te a
pro
port
ion
th
at
can
be u
sed
to d
ete
rmin
e t
he h
eig
ht
of
the l
igh
thou
se.
b.
Wh
at
is t
he h
eig
ht
of
the l
igh
thou
se?
yes;
△JA
K ∼
△W
SY
; S
AS
Sim
ilari
ty
△LM
N ∼
△P
QN
; M
L =
12;
QP
= 8
△
JLN
∼ △
KLM
; LN
= 2
1;
LM
= 1
4
△TP
S ∼
△Q
PR
; P
S =
12;
PR
= 1
6
△E
GF ∼
△H
GI;
EG
= 6
; H
G =
8
Sam
ple
an
sw
er:
If
x =
heig
ht
of
lig
hth
ou
se,
x
−
5.2
5 =
12
8
−
8
.
84 f
tNo
. T
he t
rian
gle
s w
ou
ld b
e s
imilar
by S
AS
or
AA
. If
−−
MN
‖ −
−
PQ
.
Answers (Lesson 7-3)
Chapter 7 A9 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
22
G
len
co
e G
eo
me
try
Wo
rd
Pro
ble
m P
racti
ce
Sim
ilar
Tri
an
gle
s A
B
D
E
C
1
. C
HA
IRS
A
loca
l fu
rnit
ure
sto
re s
ell
s tw
o
vers
ion
s of
the s
am
e c
hair
: on
e f
or
ad
ult
s, a
nd
on
e f
or
chil
dre
n.
Fin
d t
he
valu
e o
f x s
uch
th
at
the c
hair
s are
sim
ilar.
18˝
16˝
X
12
˝
2
. B
OA
TIN
G T
he t
wo s
ail
boats
sh
ow
n a
re
part
icip
ati
ng i
n a
regatt
a.
Fin
d t
he
valu
e o
f x.
168.5
in.
220 in. X
in.
264 in.
40°
40°
3
. G
EO
ME
TR
Y G
eorg
ia d
raw
s a r
egu
lar
pen
tagon
an
d s
tart
s co
nn
ect
ing i
ts
vert
ices
to m
ak
e a
5-p
oin
ted
sta
r. A
fter
dra
win
g t
hre
e o
f th
e
lin
es
in t
he s
tar,
sh
e
beco
mes
curi
ou
s
abou
t tw
o t
rian
gle
s
that
ap
pear
in t
he
figu
re, △ABC
an
d
△CEB
. T
hey l
ook
sim
ilar
to h
er.
Pro
ve
that
this
is
the c
ase
.
4. S
HA
DO
WS
A
rad
io t
ow
er
cast
s a
shad
ow
8 f
eet
lon
g a
t th
e s
am
e t
ime
that
a v
ert
ical
yard
stic
k c
ast
s a s
had
ow
half
an
in
ch l
on
g.
How
tall
is
the r
ad
io
tow
er?
5. M
OU
NT
AIN
PE
AK
S G
avin
an
d B
rian
na
wan
t to
kn
ow
how
far
a m
ou
nta
in p
eak
is f
rom
th
eir
hou
ses.
Th
ey m
easu
re t
he
an
gle
s betw
een
th
e l
ine o
f si
te t
o t
he
peak
an
d t
o e
ach
oth
er’
s h
ou
ses
an
d
care
full
y m
ak
e t
he d
raw
ing s
how
n.
Gavin
Bri
anna
Peak
2 in.
2.0
15 in.
0.2
46 in.
90˚
83˚
Th
e a
ctu
al
dis
tan
ce b
etw
een
Gavin
an
d
Bri
an
na’s
hou
ses
is 1
1 − 2 m
iles.
a.
Wh
at
is t
he a
ctu
al
dis
tan
ce o
f th
e
mou
nta
in p
eak
fro
m G
avin
’s h
ou
se?
Rou
nd
you
r an
swer
to t
he n
eare
st
ten
th o
f a m
ile.
b.
Wh
at
is t
he a
ctu
al
dis
tan
ce o
f th
e
mou
nta
in p
eak
fro
m B
rian
na’s
hou
se?
Rou
nd
you
r an
swer
to t
he n
eare
st
ten
th o
f a m
ile.
7-3
13.5
in
.
202.2
in
.
S
am
ple
an
sw
er:
m∠
AD
B =
108,
so
m∠
DB
A =
36 (
base o
f is
o-
scele
s △
AB
D).
Th
us,
m∠
AB
C =
72.
Sim
ilarl
y,
m∠
DC
B =
36 a
nd
m∠
AC
B =
72.
So
, m∠
BE
C =
72
an
d m∠
BA
C =
36.
Th
ere
fore
,
△A
BC
an
d △
BC
E a
re s
imilar.
576 f
t
12.2
mi
12.3
mi
Lesson 7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
23
G
len
co
e G
eo
me
try
Mo
vin
g S
had
ow
s
Have y
ou
ever
watc
hed
you
r sh
ad
ow
as
you
walk
ed
alo
ng t
he s
treet
at
nig
ht
an
d o
bse
rved
how
its
sh
ap
e c
han
ges
as
you
move?
Su
pp
ose
a m
an
wh
o i
s 6 f
eet
tall
is
stan
din
g b
elo
w
a l
am
pp
ost
th
at
is 2
0 f
eet
tall
. T
he m
an
is
walk
ing a
way f
rom
th
e l
am
pp
ost
at
a r
ate
of
5 f
eet
per
seco
nd
.
1
. If
th
e m
an
is
movin
g a
t a r
ate
of
5 f
eet
per
seco
nd
, m
ak
e a
con
ject
ure
as
to t
he r
ate
that
his
sh
ad
ow
is
movin
g.
2
. H
ow
far
aw
ay f
rom
th
e l
am
pp
ost
is
the m
an
aft
er
8 s
eco
nd
s?
3
. H
ow
far
is t
he e
nd
of
his
sh
ad
ow
fro
m t
he b
ott
om
of
the l
am
pp
ost
aft
er
8 s
eco
nd
s? U
se s
imil
ar
tria
ngle
s to
solv
e t
his
pro
ble
m.
4
. A
fter
3 m
ore
seco
nd
s, h
ow
far
from
th
e l
am
pp
ost
is
the m
an
? H
ow
far
from
th
e l
am
pp
ost
is h
is s
had
ow
?
5
. H
ow
man
y f
eet
did
th
e m
an
move i
n 3
seco
nd
s? H
ow
man
y f
eet
did
th
e s
had
ow
move i
n
3 s
eco
nd
s?
6
. T
he m
an
is
movin
g a
t a r
ate
of
5 f
eet/
seco
nd
. W
hat
rate
is
his
sh
ad
ow
movin
g?
How
does
this
rate
com
pare
to t
he c
on
ject
ure
you
mad
e i
n E
xerc
ise 1
? M
ak
e a
con
ject
ure
as
to
wh
y t
he r
esu
lts
are
lik
e t
his
.
20
ft
6 f
t
x f
t
5 f
t/sec
En
ric
hm
en
t7
-3
S
am
ple
an
sw
er:
His
sh
ad
ow
is
mo
vin
g m
ore
qu
ickly
th
an
he i
s.
4
0 f
t
5
7.1
4 f
t
5
5 f
t; 7
8.5
7 f
t
1
5 f
t; 2
1.4
3 f
t
7
.14 f
t /s;
Sam
ple
an
sw
er:
Th
e a
nsw
er
is c
on
sis
ten
t w
ith
th
e c
on
jectu
re
fro
m E
xerc
ise 1
. H
is s
had
ow
is g
ett
ing
lo
ng
er
as h
e m
oves f
urt
her
aw
ay
fro
m t
he l
am
pp
ost.
Answers (Lesson 7-3)
Chapter 7 A10 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
24
G
len
co
e G
eo
me
try
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Para
llel
Lin
es a
nd
Pro
po
rtio
nal
Part
s
Pro
po
rtio
na
l P
art
s w
ith
in T
ria
ng
les
In a
ny t
rian
gle
, a
lin
e p
ara
llel
to o
ne s
ide o
f a t
rian
gle
sep
ara
tes
the o
ther
two
sid
es
pro
port
ion
all
y.
Th
is i
s th
e T
rian
gle
Pro
port
ion
ali
ty T
heore
m.
Th
e c
on
vers
e i
s als
o t
rue.
If
"#
XY
‖
"#
RS
, th
en
RX
−
XT
= S
Y
−
YT
. If
RX
−
XT
= S
Y
−
YT
, th
en
"#
X
Y ‖
"#
R
S .
If X
an
d Y
are
th
e m
idp
oin
ts o
f −
−
RT
an
d −−
S
T ,
then
−−
XY
is
a
mid
se
gm
en
t of
the t
rian
gle
. T
he T
rian
gle
Mid
segm
en
t T
heore
m
state
s th
at
a m
idse
gm
en
t is
para
llel
to t
he t
hir
d s
ide a
nd
is
half
its
len
gth
.
If −
−
XY
is
a m
idse
gm
en
t, t
hen
"#
X
Y ‖
"#
R
S a
nd
XY
= 1
−
2 R
S.
YS
T
R
X
In
△A
BC
, −
−
EF
‖ −
−
CB
. F
ind
x.
F
C
BA
18
x+
22
x+
2
6E
Sin
ce −
−
EF
‖ −−
− C
B ,
AF
−
FB
= A
E
−
EC
.
x
+ 2
2
−
x +
2
= 1
8
−
6
6x +
132 =
18
x +
36
96 =
12x
8 =
x
In
△G
HJ
, H
K =
5,
KG
= 1
0, a
nd
JL
is o
ne
-ha
lf t
he
le
ng
th
of
−−
LG
. Is
−−
−
HK
‖ −
−
KL
?
Usi
ng t
he c
on
vers
e o
f th
e T
rian
gle
Pro
port
ion
ali
ty T
heore
m,
show
th
at
HK
−
KG
= J
L
−
LG
.
Let
JL
= x
an
d L
G =
2 x
.
HK
−
KG
= 5
−
10 =
1 −
2
JL
−
LG
= x
−
2x =
1 −
2
Sin
ce 1
−
2 =
1 −
2 ,
the s
ides
are
pro
port
ion
al
an
d
−−−
HJ
‖ −
−
KL
.
Exerc
ises
ALG
EB
RA
F
ind
th
e v
alu
e o
f x.
1.
5
5x
7
2.
9
20
x
18
3.
35x
4.
30
10
24
x
5.
11
x+
12
x33
6.
30
10
x+
10
x
7-4
Exam
ple
1Exam
ple
2
710
17.5
812
5
Lesson 7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
25
G
len
co
e G
eo
me
try
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Para
llel
Lin
es a
nd
Pro
po
rtio
nal
Part
s
Pro
po
rtio
na
l P
art
s w
ith
Pa
rall
el
Lin
es
Wh
en
th
ree o
r m
ore
para
llel
lin
es
cut
two t
ran
svers
als
, th
ey s
ep
ara
te t
he t
ran
svers
als
in
to p
rop
ort
ion
al
part
s. I
f th
e r
ati
o o
f th
e p
art
s is
1,
then
th
e p
ara
llel
lin
es
sep
ara
te t
he t
ran
svers
als
in
to c
on
gru
en
t p
art
s.
If
ℓ1 ‖
ℓ2 ‖
ℓ3,
If
ℓ4 ‖
ℓ5 ‖
ℓ6 a
nd
th
en
a −
b =
c −
d .
u −
v =
1,
then
w
−
x
= 1
.
R
efe
r t
o l
ine
s ℓ
1,
ℓ2,
an
d ℓ
3 a
bo
ve
. If
a =
3,
b =
8,
an
d c
= 5
, fi
nd
d.
ℓ 1 ‖
ℓ2 ‖
ℓ3 s
o 3
−
8 =
5 −
d .
Th
en
3d
= 4
0 a
nd
d =
13 1
−
3 .
Exerc
ises
ALG
EB
RA
F
ind
x a
nd
y.
1
.
x+
12
12
3x
5x
2
. 2
x-
6
x+
3
12
3
.
2x
+ 4
3x
- 1
2y
+ 2
3y
4.
5
8y
+ 2
y
5
. 3
4
x+
4x
6
. 1
63
2
y+
3y
a
bd
uv
xw
ct
n
m
sℓ 1
ℓ 4ℓ 5
ℓ 6
ℓ 2 ℓ 3
7-4 Exam
ple
x =
8
x =
9
x =
5;
y =
2
y =
3 1
−
3
x =
12
y =
3
Answers (Lesson 7-4)
Chapter 7 A11 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
26
G
len
co
e G
eo
me
try
1. If
JK
= 7
, K
H =
21,
an
d J
L =
6,
2
. If
RU
= 8
, U
S =
14,
TV
= x
- 1
,
fin
d L
I.
an
d V
S =
17.5
, fi
nd
x a
nd
TV
.
De
term
ine
wh
eth
er −
−
BC
‖ −
−
DE
. J
usti
fy y
ou
r a
nsw
er.
3. A
D =
15,
DB
= 1
2,
AE
= 1
0,
an
d E
C =
8
yes;
AD
−
DB
= A
E
−
EC
= 5
−
4
4. B
D =
9,
BA
= 2
7,
an
d C
E =
1
−
3 E
A
n
o;
BD
−
DA
≠ C
E
−
EA
5. A
E =
30,
AC
= 4
5,
an
d A
D =
2D
B
yes;
AE
−
EC
= A
D
−
DB
= 2
−
1
−−
JH
is a
mid
se
gm
en
t o
f △
KL
M.
Fin
d t
he
va
lue
of
x.
6.
30
x
7.
9
x
8.
8
x
ALG
EB
RA
F
ind
x a
nd
y.
9
.
2x
+ 1
3y
- 8
y+
5x
+ 7
1
0.
3 – 2x
+ 2
x+
3
2y
- 1
3y
- 5
CB
ED
A
R
UV
T
S
HL
KJ
I
1
8
11;
10
x =
6,
y =
6.5
x =
2,
y =
4
Sk
ills
Practi
ce
Para
llel
Lin
es a
nd
Pro
po
rtio
nal
Part
s
7-4
15
18
8
Lesson 7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
27
G
len
co
e G
eo
me
try
Practi
ce
Para
llel
Lin
es a
nd
Pro
po
rtio
nal
Part
s
1
. If
AD
= 2
4,
DB
= 2
7,
an
d E
B =
18,
2
. If
QT
= x
+ 6
, S
R =
12,
PS
= 2
7,
an
d
fin
d C
E.
T
R =
x -
4,
fin
d Q
T a
nd
TR
.
De
term
ine
wh
eth
er −
−
JK
‖ −
−−
NM
. J
usti
fy y
ou
r a
nsw
er.
3
. J
N =
18,
JL
= 3
0,
KM
= 2
1,
an
d M
L =
35
4
. K
M =
24,
KL
= 4
4,
an
d N
L =
5
−
6 J
N
−−
JH
is a
mid
se
gm
en
t o
f △
KL
M.
Fin
d t
he
va
lue
of
x.
5.
22
x
6
.
x+
7
x
7
. F
ind
x a
nd
y.
8. F
ind
x a
nd
y.
3x
- 4
2 – 3y
+ 3
1 – 3y
+ 6
5 – 4x
+ 3
4 – 3y
+ 2
3x
- 4
x+
1
4y
- 4
9
. M
AP
S O
n a
map
, W
ilm
ingto
n S
treet,
Beech
Dri
ve,
an
d A
sh G
rove
Lan
e a
pp
ear
to a
ll b
e p
ara
llel.
Th
e d
ista
nce
fro
m W
ilm
ingto
n t
o
Ash
Gro
ve a
lon
g K
en
dall
is
820 f
eet
an
d a
lon
g M
agn
oli
a,
660 f
eet.
If t
he d
ista
nce
betw
een
Beech
an
d A
sh G
rove a
lon
g M
agn
oli
a i
s
280 f
eet,
wh
at
is t
he d
ista
nce
betw
een
th
e t
wo s
treets
alo
ng
Ken
dall
?
Ash
Gro
ve
Bee
ch
Mag
no
liaK
end
all
Wilm
ing
ton
NL
J
KM
S
Q
T
RP
D
EC
BA
7-4
1
6
QT =
18;
TR
= 8
no
; 1
8
−
12 ≠
21
−
35
yes;
24
−
20 =
6
−
5
x
= 4
, y =
9x =
5
−
2 ,
y =
9
−
4
ab
ou
t 348 f
t
1
1
7
Answers (Lesson 7-4)
Chapter 7 A12 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
28
G
len
co
e G
eo
me
try
Wo
rd
Pro
ble
m P
racti
ce
Para
llel
Lin
es a
nd
Pro
po
rtio
nal
Part
s
Mee
eeow
ww
!
30 f
t
40 f
t
46 f
tx
8 f
t8 f
t
10 f
t
24 ft
10 f
t
x
Cay
St.
1 k
m1.4
km
0.8
km
Bay
St.
Dale St.
Earl S
t.
(not
dra
wn t
o s
cale
)
x
1
. C
AR
PE
NT
RY
Jak
e i
s
fixin
g a
n A
-fra
me.
He w
an
ts t
o a
dd
a
hori
zon
tal
sup
port
beam
half
way u
p
an
d p
ara
llel
to
the g
rou
nd
. H
ow
lon
g s
hou
ld t
his
beam
be?
2
. S
TR
EE
TS
In
th
e d
iagra
m,
Cay S
treet
an
d B
ay S
treet
are
para
llel.
Fin
d x
.
3
. JU
NG
LE
GY
MS
P
rass
ad
is
bu
ild
ing a
two-s
tory
ju
ngle
gym
acc
ord
ing t
o t
he
pla
ns
show
n.
Fin
d x
.
4
. FIR
EM
EN
A
cat
is s
tuck
in
a t
ree
an
d f
irem
en
try
to
resc
ue i
t. B
ase
d
on
th
e f
igu
re,
if a
fire
man
cli
mbs
to t
he t
op
of
the
lad
der,
how
far
aw
ay i
s th
e c
at?
5
. E
QU
AL P
AR
TS
N
ick
has
a s
tick
th
at
he
wou
ld l
ike t
o d
ivid
e i
nto
9 e
qu
al
part
s.
He p
lace
s it
on
a p
iece
of
gri
d p
ap
er
as
show
n.
Th
e g
rid
pap
er
is r
ule
d s
o t
hat
vert
ical
an
d h
ori
zon
tal
lin
es
are
equ
all
y
space
d.
a.
Exp
lain
how
he c
an
use
th
e g
rid
pap
er
to h
elp
him
fin
d w
here
he
need
s to
cu
t th
e s
tick
.
b.
Su
pp
ose
Nic
k w
an
ts t
o d
ivid
e h
is
stic
k i
nto
5 e
qu
al
part
s u
tili
zin
g t
he
gri
d p
ap
er.
Wh
at
can
he d
o?
8 f
eet
7-4 4
ft
1.1
2 k
m
13 f
t 4 i
n.
34.5
ft
B
ecau
se h
e p
osit
ion
ed
th
e
sti
ck s
o t
hat
its e
nd
s a
re
tou
ch
ing
ho
rizo
nta
l lin
es t
hat
are
9 u
nit
s a
part
, h
e c
an
cu
t
the s
tick w
here
ver
oth
er
ho
rizo
nta
l lin
es i
nte
rsect
it.
H
e c
an
ro
tate
th
e s
tick s
o i
t
tou
ch
es h
ori
zo
nta
l lin
es 5
un
its
ap
art
an
d a
pp
ly t
he s
am
e
meth
od
.
Lesson 7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
29
G
len
co
e G
eo
me
try
En
ric
hm
en
t
Para
llel
Lin
es a
nd
Co
ng
ruen
t P
art
s
Th
ere
is
a t
heore
m s
tati
ng t
hat
if t
hre
e p
ara
llel
lin
es
cut
off
con
gru
en
t se
gm
en
ts o
n o
ne
tran
svers
al,
th
en
th
ey c
ut
off
con
gru
en
t se
gm
en
ts o
n a
ny t
ran
svers
al.
Th
is c
an
be s
how
n
for
an
y n
um
ber
of
para
llel
lin
es.
Th
e f
oll
ow
ing d
raft
ing t
ech
niq
ue u
ses
this
fact
to d
ivid
e a
segm
en
t in
to c
on
gru
en
t p
art
s.
−−
AB
to b
e s
ep
ara
ted
in
to f
ive c
on
gru
en
t p
art
s. T
his
can
be
don
e v
ery
acc
ura
tely
wit
hou
t u
sin
g a
ru
ler.
All
th
at
is n
eed
ed
is a
com
pass
an
d a
pie
ce o
f n
ote
book
pap
er.
Ste
p 1
H
old
th
e c
orn
er
of
a p
iece
of
note
book
pap
er
at
poin
t A
.
Ste
p 2
F
rom
poin
t A
, d
raw
a s
egm
en
t alo
ng t
he p
ap
er
that
is f
ive s
pace
s lo
ng.
Mark
wh
ere
th
e l
ines
of
the n
ote
book
pap
er
meet
the s
egm
en
t. L
abel
the f
ifth
poin
t P
.
Ste
p 3
D
raw
−−
PB
. T
hro
ugh
each
of
the o
ther
mark
s
on
−−
AP
, co
nst
ruct
a l
ine p
ara
llel
to −
−
BP
. T
he
poin
ts w
here
th
ese
lin
es
inte
rsect
−−
AB
wil
l
div
ide −
−
AB
in
to f
ive c
on
gru
en
t se
gm
en
ts.
Use
a c
om
pa
ss a
nd
a p
iece
of
no
teb
oo
k p
ap
er t
o d
ivid
e
ea
ch
se
gm
en
t in
to t
he
giv
en
nu
mb
er o
f co
ng
ru
en
t p
arts
.
1
. si
x c
on
gru
en
t p
art
s
2
. se
ven
con
gru
en
t p
art
s
AB
AB
A
P
B
AB
P
AB
AB
7-4
See s
tud
en
ts’
wo
rk.
Answers (Lesson 7-4)
Chapter 7 A13 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
30
G
len
co
e G
eo
me
try
7-5
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Part
s o
f S
imilar
Tri
an
gle
s
Sp
eci
al
Se
gm
en
ts o
f S
imil
ar
Tri
an
gle
s W
hen
tw
o t
rian
gle
s are
sim
ilar,
co
rresp
on
din
g a
ltit
ud
es,
an
gle
bis
ect
ors
, an
d m
ed
ian
s are
pro
port
ion
al
to t
he c
orr
esp
on
din
g
sid
es.
Exerc
ises
Fin
d x
.
1
. x
36
18
20
2
.
69
12
x
3
.
3
3
4
x
4
.
10
10
x
8
87
5
.
45
42
x
30
6
.
14
12
12
x
Exam
ple
In
th
e f
igu
re, △ABC
∼ △
XYZ
, w
ith
an
gle
bis
ecto
rs a
s s
ho
wn
. F
ind
x.
Sin
ce △
AB
C ∼
△X
YZ
, th
e m
easu
res
of
the a
ngle
bis
ect
ors
are
pro
port
ion
al
to
the m
easu
res
of
a p
air
of
corr
esp
on
din
g s
ides.
AB
−
XY
= B
D
−
WY
24
−
x
= 1
0
−
8
10x =
24(8
)
10
x =
19
2
x =
19.2
24
10 D
W
Y
ZX
C
B
A
8
x
10
8
2.2
58.7
5
14
28
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
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Lesson 7-5
Ch
ap
ter
7
31
G
len
co
e G
eo
me
try
7-5
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Part
s o
f S
imilar
Tri
an
gle
s
Tri
an
gle
An
gle
Bis
ect
or
Th
eo
rem
A
n a
ngle
bis
ect
or
in a
tri
an
gle
sep
ara
tes
the
op
posi
te s
ide i
nto
tw
o s
egm
en
ts t
hat
are
pro
port
ion
al
to t
he l
en
gth
s of
the o
ther
two s
ides.
F
ind
x.
Sin
ce −
−−
SU
is
an
an
gle
bis
ect
or,
RU
−
TU
= R
S
−
TS
.
x
−
20 =
15
−
30
30x =
20(1
5)
30x =
30
0
x =
10
Exerc
ises
Fin
d t
he
va
lue
of
ea
ch
va
ria
ble
.
1
. 25
20
28
x
2.
15
9
3a
3
.
36
42
46.8
n
4.
10
15
13
x
5
.
110
100
160
r
6
.
17
11
x+
7
x
Exam
ple
x2
0
30
15
UT
S
R
35
5
66
12 5
−
6
25.2
26
Answers (Lesson 7-5)
Chapter 7 A14 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
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TE
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Ch
ap
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7
32
G
len
co
e G
eo
me
try
7-5
Sk
ills
Practi
ce
Part
s o
f S
imilar
Tri
an
gle
sF
ind
x.
1.
2.
7 7
22
x5.2
5
5.2
5
153
3
10x
3.
4.
20
10
x
22
18
121
2.6
x
5. If
△R
ST
∼ △
EF
G,
−−
−
SH
is
an
6. If
△A
BC
∼ △
MN
P,
−−
−
AD
is
an
alt
itu
de o
f △
RS
T,
−−
FJ
is
an
alt
itu
de o
f
alt
itu
de o
f △
AB
C,
−−
−
MQ
is
an
alt
itu
de o
f
△E
FG
, S
T =
6,
SH
= 5
, an
d F
J =
7,
△M
NP
, A
B =
24,
AD
= 1
4,
an
dfi
nd
FG
. M
Q =
10.5
, fi
nd
MN
.
JG
E
F
HT
R
S
C
A
BD
PN
QM
Fin
d t
he
va
lue
of e
ach
va
ria
ble
.
7.
8.
26
12
8
m
7
20
24
x
8.4
18
16.5
22
17 1
−
3
8.4
11
17
.1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
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Lesson 7-5
Ch
ap
ter
7
33
G
len
co
e G
eo
me
try
Practi
ce
Part
s o
f S
imilar
Tri
an
gle
s
ALG
EB
RA
F
ind
x.
1
.
32
30
24
x
2.
26
25
39
x
3
.
40
2x
+ 1
25
x+
4
4.
5
. If
△J
KL
∼△
NP
R,
−−
−K
M i
s an
6
. If
△S
TU
∼△
XY
Z,
−−
−U
A i
s an
alt
itu
de o
f △
JK
L,
−−
PT
is
an
alt
itu
de
alt
itu
de o
f △
ST
U,
−−
ZB
is
an
alt
itu
de
of
△N
PR
, K
L=
28,
KM
= 1
8,
an
d
of
△X
YZ
, U
T=
8.5
, U
A=
6,
an
d
PT
= 1
5.7
5,
fin
d P
R.
Z
B=
11.4
, fi
nd
ZY
.
MJ
L
K
TN
R
P
YX
BZ
TS
AU
7
. P
HO
TO
GR
AP
HY
F
ran
cin
e h
as
a c
am
era
in
wh
ich
th
e d
ista
nce
fro
m t
he l
en
s to
th
e f
ilm
is
24 m
illi
mete
rs.
a.
If F
ran
cin
e t
ak
es
a f
ull
-len
gth
ph
oto
gra
ph
of
her
frie
nd
fro
m a
dis
tan
ce o
f 3 m
ete
rs
an
d t
he h
eig
ht
of
her
frie
nd
is
140 c
en
tim
ete
rs,
wh
at
wil
l be t
he h
eig
ht
of
the i
mage
on
th
e f
ilm
? (H
int:
Con
vert
to t
he s
am
e u
nit
of
measu
re.)
b.
Su
pp
ose
th
e h
eig
ht
of
the i
mage o
n t
he f
ilm
of
her
frie
nd
is
15 m
illi
mete
rs.
If
Fra
nci
ne t
ook
a f
ull
-len
gth
sh
ot,
wh
at
was
the d
ista
nce
betw
een
th
e c
am
era
an
d h
er
frie
nd
?
7-5
x
28
20
30
22.5
16.7
24.5
16.1
5
13.5
16.8
11.2
mm
2.2
4 m
Answers (Lesson 7-5)
Chapter 7 A15 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
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RIO
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Ch
ap
ter
7
34
G
len
co
e G
eo
me
try
Wo
rd
Pro
ble
m P
racti
ce
Part
s o
f S
imilar
Tri
an
gle
s
1
. FLA
GS
An
oce
an
lin
er
is f
lyin
g t
wo
sim
ilar
tria
ngu
lar
flags
on
a f
lag p
ole
.
Th
e a
ltit
ud
e o
f th
e l
arg
er
flag i
s th
ree
tim
es
the a
ltit
ud
e o
f th
e s
mall
er
flag.
If
the m
easu
re o
f a l
eg o
n t
he l
arg
er
flag i
s
45 i
nch
es,
fin
d t
he m
easu
re o
f th
e
corr
esp
on
din
g l
eg o
n t
he s
mall
er
flag.
2
. T
EN
TS
Jan
a w
en
t ca
mp
ing a
nd
sta
yed
in a
ten
t sh
ap
ed
lik
e a
tri
an
gle
. In
a
ph
oto
of
the t
en
t, t
he b
ase
of
the t
en
t is
6 i
nch
es
an
d t
he a
ltit
ud
e i
s 5 i
nch
es.
Th
e a
ctu
al
base
was
12 f
eet
lon
g.
Wh
at
was
the h
eig
ht
of
the a
ctu
al
ten
t?
x
3
. P
LA
YG
RO
UN
D T
he p
laygro
un
d a
t
Han
k’s
sch
ool
has
a l
arg
e r
igh
t tr
ian
gle
pain
ted
in
th
e g
rou
nd
. H
an
k s
tart
s
at
the r
igh
t an
gle
corn
er
an
d w
alk
s
tow
ard
th
e o
pp
osi
te s
ide a
lon
g a
n a
ngle
bis
ect
or
an
d s
top
s w
hen
he g
ets
to t
he
hyp
ote
nu
se.
A
B
45˚
30
ft
40 f
t
50 ft
How
mu
ch f
art
her
from
Han
k i
s p
oin
t B
vers
us
poin
t A
?
4. FLA
G P
OLE
S A
fla
g p
ole
att
ach
ed
to t
he
sid
e o
f a b
uil
din
g i
s su
pp
ort
ed
wit
h
a n
etw
ork
of
stri
ngs
as
show
n i
n t
he
figu
re.
AB
C
DF E
Th
e r
iggin
g i
s d
on
e s
o t
hat
AE
=E
F,
AC
=C
D,
an
d A
B=
BC
. W
hat
is t
he
rati
o o
f C
F t
o B
E?
5
. C
OP
IES
G
ord
on
mad
e a
ph
oto
cop
y o
f a
page f
rom
his
geom
etr
y b
ook
to e
nla
rge
on
e o
f th
e f
igu
res.
Th
e a
ctu
al
figu
re t
hat
he c
op
ied
is
show
n b
elo
w.
39 m
m
Median
Altitude
30 m
m
29
mm
Th
e p
hoto
cop
y c
am
e o
ut
poorl
y.
Gord
on
cou
ld n
ot
read
th
e n
um
bers
on
th
e
ph
oto
cop
y,
alt
hou
gh
th
e t
rian
gle
its
elf
was
clear.
Gord
on
measu
red
th
e b
ase
of
the e
nla
rged
tri
an
gle
an
d f
ou
nd
it
to b
e
200 m
illi
mete
rs.
a
. W
hat
is t
he l
en
gth
of
the d
raw
n
alt
itu
de o
f th
e e
nla
rged
tri
an
gle
?
Rou
nd
you
r an
swer
to t
he n
eare
st
mil
lim
ete
r.
b
. W
hat
is t
he l
en
gth
of
the d
raw
n
med
ian
of
the e
nla
rged
tri
an
gle
?
Rou
nd
you
r an
swer
to t
he n
eare
st
mil
lim
ete
r.
7-5 1
5 i
nch
es
10 f
t
7 1
−
7 f
t
2 :1 1
49 m
m
154 m
m
Lesson 7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
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Ch
ap
ter
7
35
G
len
co
e G
eo
me
try
A P
roo
f o
f P
yth
ag
ore
an
Th
eo
rem
1. F
or
righ
t tr
ian
gle
AB
C w
ith
rig
ht
an
gle
C,
an
d
alt
itu
de −
−−
CD
as
show
n a
t th
e r
igh
t, n
am
e t
hre
e
sim
ilar
tria
ngle
s.
2
. L
ist
the t
hre
e s
imil
ar
tria
ngle
s as
head
ings
in
the t
able
belo
w.
Use
th
e f
igu
re t
o c
om
ple
te t
he
table
to l
ist
the c
orr
esp
on
din
g p
art
s of
the t
hre
e
sim
ilar
righ
t tr
ian
gle
s.
△A
BC
△A
CD
△C
BD
Sh
ort
Le
ga
hd
Lo
ng
Le
gb
eh
Hy
po
ten
us
ec
ba
3
. U
se t
he c
orr
esp
on
din
g p
art
s of
these
sim
ilar
tria
ngle
s an
d t
heir
pro
port
ion
s
to c
om
ple
te t
he s
tate
men
ts i
n t
he p
roof
an
d a
lgebra
icall
y p
rove t
he
Pyth
agore
an
Th
eore
m.
S
ta
te
me
nts
Re
aso
ns
1.
Rig
ht
tria
ngle
AB
C w
ith
1
. G
iven
alt
itu
de −
−−
CD
.
2
.
2.
Corr
esp
on
din
g p
art
s of
sim
ilar
tria
ngle
s are
in
th
e s
am
e r
ati
o.
3
.
3.
Cro
ss P
rod
uct
s P
rop
ert
y
4
.
4.
Ad
dit
ion
Pro
pert
y o
f E
qu
ali
ty
5
.
5.
Su
bst
itu
tion
6
.
6.
Dis
trib
uti
ve P
rop
ert
y
7
.
7.
Segm
en
t ad
dit
ion
8
. a
2 +
b2 =
c2
8.
Su
bst
itu
tion
A
ab
h
de
c
B
C D
En
ric
hm
en
t7
-5
△
AB
C ∼
△A
CD
∼ △
CB
D
a2 =
cd
, b
2 =
ce
a2 +
b2 =
cd
+ b
2
a2 +
b2 =
cd
+ c
e
a2 +
b2 =
c(d
+ e
)
d +
e =
c
a
−
c =
d
−
a ,
b
−
c =
e
−
b
Answers (Lesson 7-5)
Chapter 7 A16 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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Ch
ap
ter
7
36
G
len
co
e G
eo
me
try
You
can
use
a s
pre
ad
sheet
to c
reate
a S
ierp
insk
i tr
ian
gle
.
U
se
a s
pre
ad
sh
ee
t to
cre
ate
a S
ierp
insk
i tr
ian
gle
.
Ste
p 1
In
cell
A2,
en
ter
1.
In c
ell
A3,
en
ter
an
equ
als
sig
n f
oll
ow
ed
by A
2 +
1 . T
his
wil
l re
turn
th
e n
um
ber
of
itera
tion
s. C
lick
on
th
e b
ott
om
rig
ht
corn
er
of
cell
A2 a
nd
d
rag i
t th
rou
gh
cell
A500 t
o g
et
500 i
tera
tion
s.
Ste
p 2
In
cell
B1,
en
ter
0.5
. T
his
in
dic
ate
s th
e m
idp
oin
ts o
f th
e s
egm
en
ts.
Ste
p 3
In
cell
C1,
en
ter
1 a
nd
in
cell
D1,
en
ter
0.3
.
Ste
p 4
In
cell
B2,
en
ter
an
equ
als
sig
n f
oll
ow
ed
by 3
*R
AN
D()
. C
lick
on
th
e b
ott
om
rig
ht
corn
er
of
cell
B2 a
nd
dra
g i
n t
hro
ugh
cell
B500 t
o g
et
500 i
tera
tion
s.
Ste
p 5
In
cell
C2,
en
ter
an
equ
als
sig
n f
oll
ow
ed
by t
he r
ecu
rsiv
e f
orm
ula
IF
(B2
<1,(
12
$B
$1)*
C1,I
F(B
2<
2,(
1-
$B
$1)*
C1
+$B
$1,(
1-
$B
$1)*
C1
+2
*$B
$1))
. T
his
w
ill
retu
rn t
he x
valu
es
of
the p
oin
ts t
o b
e g
rap
hed
. C
lick
on
th
e b
ott
om
rig
ht
corn
er
of
cell
C2 a
nd
dra
g t
hro
ugh
cell
C500.
Ste
p 6
In
cell
D2,
en
ter
an
equ
als
sig
n f
oll
ow
ed
by t
he r
ecu
rsiv
e f
orm
ula
IF
(B2
<1,(
1-
$B
$1)*
D1,I
F(B
2<
2,(
1-
$B
$1)*
D1
+$B
$1,(
1-
$B
$1)*
D1))
. T
his
wil
l re
turn
th
e y
valu
es
of
the p
oin
ts t
o b
e g
rap
hed
. C
lick
on
th
e b
ott
om
rig
ht
corn
er
of
cell
D2 a
nd
dra
g t
hro
ugh
ce
ll D
500.
Ste
p 7
T
o g
rap
h t
he v
alu
es
in
colu
mn
s C
an
d D
, fi
rst
hig
hli
gh
t all
of
the d
ata
in
th
e t
wo c
olu
mn
s. N
ext,
ch
oose
th
e c
hart
wiz
ard
fr
om
th
e t
oolb
ar.
Sele
ct X
Y
(Sca
tter)
. P
ress
Next,
Next.
T
hen
sele
ct t
he G
rid
lin
es
tab a
nd
un
check
th
e M
ajo
r gri
dli
nes.
Th
en
pre
ss N
ext
an
d F
inis
h.
Th
is w
ill
retu
rn t
he S
ierp
insk
i tr
ian
gle
.
Exerc
ises
An
aly
ze
yo
ur d
ra
win
g.
1
. W
hat
hap
pen
s to
you
r d
raw
ing i
f you
have m
ore
ite
rati
on
s? T
ry 1
000,
2000,
an
d 5
000.
2
. C
han
ge t
he 0
.5 t
o 2
/3 i
n c
ell
B1.
(Hin
t: Y
ou
may n
eed
to e
nte
r 0.6
66666 f
or
2/3
.) H
ow
d
oes
this
ch
an
ge t
he p
ictu
re?
3
. C
han
ge 0
.3 t
o 0
.6 i
n c
ell
D1.
How
does
this
ch
an
ge t
he d
raw
ing?
4
. E
nte
r th
e f
oll
ow
ing i
nto
a n
ew
sp
read
sheet
an
d d
esc
ribe w
hat
you
see.
S
tep
1:
In c
ell
A2, en
ter
the f
orm
ula
= A
1.
S
tep
2:
In c
ell
B2, en
ter
the f
orm
ula
= A
1 +
B1.
S
tep
3:
Cli
ck o
n t
he b
ott
om
rig
ht
corn
er
of
cell
B2 a
nd
dra
g t
hro
ugh
cell
L2.
S
tep
4:
Fir
st, cl
ick
on
th
e 2
next
to c
ell
A2. T
hen
, cl
ick
on
th
e b
ott
om
left
corn
er
of
2
an
d d
rag d
ow
n t
hro
ugh
cell
12.
S
tep
5:
In c
ell
A1, en
ter
a 1
an
d p
ress
EN
TE
R.
Sh
ee
t 1
Sh
ee
t 2
Sh
ee
t 3
Th
e p
ictu
re l
oo
ks s
harp
er
wit
h m
ore
ite
rati
on
s.
See s
tud
en
ts’
wo
rk.
See s
tud
en
ts’
wo
rk.
Pascal’s t
rian
gle
Sp
read
sheet
Act
ivit
y
Fra
cta
ls
7-5 Exam
ple
Lesson 7-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
37
G
len
co
e G
eo
me
try
7-6
Ide
nti
fy S
imil
ari
ty T
ran
sfo
rma
tio
ns
A d
ila
tio
n i
s a t
ran
sform
ati
on
th
at
en
larg
es
or
red
uce
s th
e o
rigin
al
figu
re p
rop
ort
ion
all
y.
Th
e s
ca
le f
acto
r o
f a
dil
ati
on
, k,
is t
he r
ati
o
of
a l
en
gth
on
th
e i
mage t
o a
corr
esp
on
din
g l
en
gth
on
th
e p
reim
age.
A d
ilati
on
wit
h k
> 1
is
an
en
larg
em
en
t. A
dil
ati
on
wit
h 0
< k
< 1
is
a r
ed
ucti
on
.
D
ete
rm
ine
wh
eth
er t
he
dil
ati
on
fro
m A
to
B i
s a
n enlargement
or a
reduction
. T
he
n f
ind
th
e s
ca
le f
acto
r o
f th
e d
ila
tio
n.
Exerc
ises
De
term
ine
wh
eth
er t
he
dil
ati
on
fro
m A
to
B i
s a
n enlargement
or a
reduction
.
Th
en
fin
d t
he
sca
le f
acto
r o
f th
e d
ila
tio
n.
1.
y
x
2.
y
x
3
. y
x
4.
y
x
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sim
ilari
ty T
ran
sfo
rmati
on
s
Exam
ple
a.
y
x
B i
s la
rger
than
A,
so t
he d
ilati
on
is
an
en
larg
em
en
t.
Th
e d
ista
nce
betw
een
th
e v
ert
ices
at
(-3,
4)
an
d (
-1,
4)
for
A i
s 2.
Th
e
dis
tan
ce b
etw
een
th
e v
ert
ices
at
(0,
3)
an
d (
4,
3)
for
B i
s 4.
Th
e s
cale
fact
or
is 4
−
2 o
r 2.
b.
y
x
B i
s sm
all
er
than
A,
so t
he d
ilati
on
is
a
red
uct
ion
.
Th
e d
ista
nce
betw
een
th
e v
ert
ices
at
(2,
3)
an
d
(2,
-3)
for
A i
s 6.
Th
e d
ista
nce
betw
een
th
e
vert
ices
at
(2,
1)
an
d (
2,
-2)
for
B i
s 3.
Th
e s
cale
fact
or
is 3
−
6 o
r 1
−
2 .
e
nla
rgem
en
t; 2
r
ed
ucti
on
; 1
−
2
r
ed
ucti
on
; 4
−
5
red
ucti
on
; 1
−
2
Answers (Lesson 7-5 and Lesson 7-6)
Chapter 7 A17 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
38
G
len
co
e G
eo
me
try
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Sim
ilari
ty T
ran
sfo
rmati
on
s
Ve
rify
Sim
ila
rity
Y
ou
can
veri
fy t
hat
a d
ilati
on
pro
du
ces
a s
imil
ar
figu
re b
y c
om
pari
ng
the r
ati
os
of
all
corr
esp
on
din
g s
ides.
For
tria
ngle
s, y
ou
can
als
o u
se S
AS
Sim
ilari
ty.
G
ra
ph
th
e o
rig
ina
l fi
gu
re
an
d i
ts d
ila
ted
im
ag
e.
Th
en
ve
rif
y t
ha
t th
e d
ila
tio
n i
s a
sim
ila
rit
y t
ra
nsfo
rm
ati
on
.
Exam
ple
a.
orig
ina
l: A
(-3
, 4
), B
(2,
4),
C(-
3, -
4)
im
ag
e: D
(1,
0),
E(3
.5,
0),
F(1
, -
4)
Gra
ph
each
fig
ure
. S
ince
∠A
an
d ∠D
are
both
rig
ht
an
gle
s, ∠A
" ∠D
. S
how
th
at
the l
en
gth
s of
the s
ides
that
incl
ud
e
∠A
an
d ∠D
are
pro
port
ion
al
to p
rove
sim
ilari
ty b
y S
AS
.
Use
th
e c
oord
inate
gri
d t
o f
ind
th
e
len
gth
s of
vert
ical
segm
en
ts A
C a
nd
DF
an
d h
ori
zon
tal
segm
en
ts A
B a
nd
DE
.
AC
−
DF
= 8
−
4 =
2 a
nd
AB
−
DE
=
5
−
2.5
= 2
,
so A
C
−
DF
= A
B
−
DE
.
Sin
ce t
he l
en
gth
s of
the s
ides
that
incl
ud
e
∠A
an
d ∠D
are
pro
port
ion
al,
△A
BC
∼
△D
EF
by S
AS
sim
ilari
ty.
b.
orig
ina
l: G
(-4
, 1
), H
(0,
4),
J(4
, 1
), K
(0, -
2)
im
ag
e: L
(-2
, 1
.5),
M(0
, 3
), N
(2,
1.5
), P
(0,
0)
Use
th
e d
ista
nce
form
ula
to f
ind
th
e l
en
gth
of
each
sid
e.
GH
= √
''
'
42 +
32 =
√ '
'
25 =
5
HJ
= √
''
'
42 +
32 =
√ '
'
25 =
5
JK
= √
''
'
42 +
32 =
√ '
'
25 =
5
KG
= √
''
'
42 +
32 =
√ '
'
25 =
5
LM
= √
''
''
22 +
1.5
2 =
√ '
'
6.2
5 =
2.5
MN
= √
''
''
22 +
1.5
2 =
√ '
'
6.2
5 =
2.5
NP
= √
''
''
22 +
1.5
2 =
√ '
'
6.2
5 =
2.5
PL
= √
''
''
22 +
1.5
2 =
√ '
'
6.2
5 =
2.5
Fin
d a
nd
com
pare
th
e r
ati
os
of
corr
esp
on
din
g
sid
es.
GH
−
LM
=
5
−
2.5
= 2
, H
J
−
MN
=
5
−
2.5
= 2
,
JK
−
NP
=
5
−
2.5
= 2
, K
C
−
PL
=
5
−
2.5
= 2
.
Sin
ce G
H
−
LM
=
HJ
−
MN
= J
K
−
NP
= K
C
−
PL
, G
HJ
K ∼
LM
NP
.
y
x
y
x
Exerc
ises
Gra
ph
th
e o
rig
ina
l fi
gu
re
an
d i
ts d
ila
ted
im
ag
e.
Th
en
ve
rif
y t
ha
t th
e d
ila
tio
n i
s a
sim
ila
rit
y t
ra
nsfo
rm
ati
on
.
1
. A
(-4,
-3),
B(2
, 5),
C(2
, -
3),
2
. P
(-4,
1),
Q(-
2,
4),
R(0
, 1),
S(-
2,
-2),
D
(-2,
-2),
E(1
, 3),
F(1
, -
2)
W
(1,
-1.5
), X
(2,
0),
Y(3
, -
1.5
), Z
(2,
-3)
7-6
S
ee s
tud
en
ts’
wo
rk.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-6
Ch
ap
ter
7
39
G
len
co
e G
eo
me
try
7-6
Dete
rm
ine w
heth
er t
he d
ila
tio
n f
ro
m A
to
B i
s a
n enlargement
or
a reduction
. T
hen
fin
d t
he s
ca
le f
acto
r o
f th
e d
ila
tio
n.
1.
y
x
2
. y
x
3.
y
x
4
. y
x
Gra
ph
th
e o
rig
ina
l fi
gu
re
an
d i
ts d
ila
ted
im
ag
e.
Th
en
ve
rif
y t
ha
t th
e d
ila
tio
n i
s a
sim
ila
rit
y t
ra
nsfo
rm
ati
on
.
5.
A(–
3,
4),
B(3
, 4),
C(–
3,
–2);
6
. F
(–3,
4),
G(2
, 4),
H(2
, –2),
J(–
3,
–2);
A'(–
2,
3),
B'(0
, 3
), C'(–
2,
1)
F'(–
1.5
, 3
), G'(1
, 3
), H'(1
, 0
), J'(–
1.5
, 0
)
Sk
ills
Pra
ctic
e
Sim
ilari
ty T
ran
sfo
rmati
on
s
′
y
x
′′
′ ′
y
x′′
7.
P(–
3,
1),
Q(–
1,
1),
R(–
1,
–3);
8
. A
(–5,
–1),
B(0
, 1),
C(5
, –1),
D(0
, –3);
P'(–
1,
4),
Q'(3
, 4
), R'(3
, –
4)
A'(1
, –
1.5
), B'(2
, 0
), C'(3
, –
1.5
), D'(2
, –
3)
′
′ ′
y
x
′ ′
′
y
x
′
e
nla
rgem
en
t; 4
−
3
en
larg
em
en
t; 7
−
3
r
ed
ucti
on
; 1
−
2
red
ucti
on
; 3
−
4
s
imilar
by S
AS
sim
ilar
by p
rop
ort
ion
al
sid
es
s
imilar
by S
AS
sim
ilar
by p
rop
ort
ion
al
sid
es
Answers (Lesson 7-6)
Chapter 7 A18 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
40
G
len
co
e G
eo
me
try
7-6
Practi
ce
Sim
ilari
ty T
ran
sfo
rmati
on
sD
ete
rm
ine
wh
eth
er t
he
dil
ati
on
fro
m A
to
B i
s a
n enlargement
or a
reduction
.
Th
en
fin
d t
he
sca
le f
acto
r o
f th
e d
ila
tio
n.
1.
y
x
2
. y
x
e
nla
rgem
en
t; 2
red
ucti
on
; 1
−
2
3
. y
x
4
. y
x
e
nla
rgem
en
t; 3
red
ucti
on
; 3
−
4
5
. y
x
6
. y
x
e
nla
rgem
en
t; 7
−
5
re
du
cti
on
; 1
−
2
Gra
ph
th
e o
rig
ina
l fi
gu
re
an
d i
ts d
ila
ted
im
ag
e.
Th
en
ve
rif
y t
ha
t th
e d
ila
tio
n i
s a
sim
ila
rit
y t
ra
nsfo
rm
ati
on
.
7
. Q
(1,
4),
R(4
, 4),
S(4
, -
1),
8
. A
(-4,
2),
B(0
, 4),
C(4
, 2),
D(0
, -
2),
X
(-4,
5),
Y(2
, 5),
Z(2
, -
5)
F
(-2,
1),
G(0
, 2),
H(2
, 1),
J(0
, -
1)
9
. FA
BR
IC R
yan
bu
ys
an
8-f
oot-
lon
g b
y 6
-foot-
wid
e p
iece
of
fabri
c as
show
n.
He w
an
ts t
o
cut
a s
mall
er,
sim
ilar
rect
an
gu
lar
pie
ce t
hat
has
a s
cale
fact
or
of k =
1
−
4 .
If p
oin
t A
(-4,
3)
is t
he t
op
left
-han
d v
ert
ex o
f both
th
e o
rigin
al
pie
ce o
f fa
bri
c an
d t
he p
iece
Ryan
wis
hes
to c
ut
ou
t, w
hat
are
th
e c
oord
inate
s of
the v
ert
ices
for
the p
iece
Ryan
wil
l cu
t?
(
-2,
3),
(-
2,
1.5
), (
-4,
1.5
)
See s
tud
en
ts’
wo
rk.
S
imilar
by S
AS
Sim
ilar
by p
rop
ort
ion
al
sid
es
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-6
Ch
ap
ter
7
41
G
len
co
e G
eo
me
try
7-6
1
. C
ITY
PLA
NN
ING
T
he s
tan
dard
siz
e o
f a
city
blo
ck i
n M
an
hatt
an
is
264 f
eet
by
900 f
eet.
Th
e c
ity p
lan
ner
of
Mech
lin
bu
rg
wan
ts t
o b
uil
d a
new
su
bd
ivis
ion
usi
ng
sim
ilar
blo
cks
so t
he d
imen
sion
s of
a
stan
dard
Man
hatt
an
blo
ck a
re e
nla
rged
by 2
.5 t
imes.
Wh
at
wil
l be t
he n
ew
d
imen
sion
s of
each
en
larg
ed
blo
ck?
660 f
eet
by 2
250 f
eet
2
. S
TO
RA
GE
SH
ED
A
loca
l h
om
e
imp
rovem
en
t st
ore
sell
s d
iffe
ren
t si
zes
of
stora
ge s
hed
s. T
he m
ost
exp
en
sive s
hed
h
as
a f
ootp
rin
t th
at
is 1
5 f
eet
wid
e b
y 2
1
feet
lon
g.
Th
e l
east
exp
en
sive s
hed
has
a
footp
rin
t th
at
is 1
0 f
eet
wid
e b
y 1
4 f
eet
lon
g.
Are
th
e f
ootp
rin
ts o
f th
e t
wo s
hed
s si
mil
ar?
If
so,
tell
wh
eth
er
the f
ootp
rin
ts
of
the l
east
exp
en
sive s
hed
is
an
en
larg
em
en
t or
a r
ed
uct
ion
, an
d f
ind
th
e
scale
fact
or
from
th
e m
ost
exp
en
sive s
hed
to
th
e l
east
exp
en
sive s
hed
.
yes;
red
ucti
on
; 2
−
3
3
. FIN
D T
HE
ER
RO
R Jere
my a
nd
Eli
sa a
re
con
stru
ctin
g d
ilati
on
s of
rect
an
gle
ABCD
for
their
geom
etr
y c
lass
. Jere
my d
raw
s an
en
larg
em
en
t FGHJ
th
at
con
tain
s th
e
poin
ts F
(-
3,
3)
an
d J
(3,
-6).
Eli
sa
dra
ws
a r
ed
uct
ion
KLMN
th
at
con
tain
s th
e p
oin
ts L
(-3,
3)
an
d N
(-2,
2).
Wh
ich
p
ers
on
mad
e a
n e
rror
in t
heir
dil
ati
on
? E
xp
lain
.
y
x
Elisa m
ad
e t
he e
rro
r; K
LM
N i
s n
ot
sim
ilar
to t
he o
rig
inal
AB
CD
.
4
. B
AN
NE
RS
T
he B
aysi
de H
igh
Sch
ool
Sp
irit
Squ
ad
is
mak
ing a
ban
ner
to t
ak
e
to a
way g
am
es.
Th
e b
an
ner
they u
se f
or
hom
e g
am
es
is s
how
n b
elo
w.
If t
he n
ew
ban
ner
is t
o b
e a
red
uct
ion
of
the h
om
e
gam
e b
an
ner
wit
h a
sca
le f
act
or
of
1 − 2 ,
wh
at
wil
l be t
he h
eig
ht
of
the n
ew
ban
ner?
13 ft
3.5
ft
1.7
5 f
t
5
. R
EA
SO
NIN
G C
on
sid
er
the i
mage QRST
of
a r
ect
an
gle
WXYZ
.
a.
Is i
t p
oss
ible
th
at
poin
t Q
an
d p
oin
t W
cou
ld h
ave t
he s
am
e c
oord
inate
s? I
f so
, w
hat
mu
st b
e t
rue a
bou
t p
oin
t Q
?
yes,
po
int
Q i
s t
he c
en
ter
of
dilati
on
.
b.
Is i
t p
oss
ible
th
at
both
poin
ts R
an
d X
cou
ld h
ave t
he s
am
e c
oord
inate
s if
p
oin
ts T
an
d Z
have t
he s
am
e
coord
inate
s? I
f so
, w
hat
are
th
e
poss
ible
valu
es
of
the s
cale
fact
or k f
or
the d
ilati
on
?
yes;
k =
1
Wo
rd
Pro
ble
m P
racti
ce
Sim
ilari
ty T
ran
sfo
rmati
on
s
Answers (Lesson 7-6)
Chapter 7 A19 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
42
G
len
co
e G
eo
me
try
7-6
En
rich
men
t
Med
ial
an
d O
rth
ic T
rian
gle
sT
he m
ed
ial
tria
ng
le i
s th
e t
rian
gle
form
ed
by c
on
nect
ing t
he
mid
poin
ts o
f each
sid
e o
f th
e t
rian
gle
. T
he t
rian
gle
form
ed
by
A’, B
’, a
nd
C’ is
th
e m
ed
ial
tria
ngle
of
tria
ngle
AB
C.
Use
a r
ule
r a
nd
co
mp
ass.
Dra
w t
he
me
dia
l tr
ian
gle
fo
r e
ach
tria
ng
le b
elo
w.
1
.
2.
3. U
se t
he t
rian
gle
s you
have c
reate
d t
o s
how
th
at
the m
ed
ial
tria
ngle
is
sim
ilar
to t
he
ori
gin
al
tria
ngle
.
S
ee s
tud
en
ts’
wo
rk.
Th
e o
rth
ic t
ria
ng
le i
s th
e t
rian
gle
form
ed
by c
on
nect
ing t
he
en
dp
oin
ts o
f each
of
the a
ltit
ud
es
of
the t
rian
gle
. T
he t
rian
gle
form
ed
by F
, D
, an
d,
E i
s th
e o
rth
ic t
rian
gle
of
tria
ngle
AB
C.
Use
a r
ule
r a
nd
co
mp
ass.
Dra
w t
he
orth
ic t
ria
ng
le f
or e
ach
tria
ng
le b
elo
w.
1
.
2.
3
. U
se t
he t
rian
gle
s you
have c
reate
d t
o s
how
th
at
the o
rth
ic t
rian
gle
is
sim
ilar
to t
he
ori
gin
al
tria
ngle
.
S
ee s
tud
en
ts’
wo
rk.
'
''
'
''
'
''
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-7
Ch
ap
ter
7
43
G
len
co
e G
eo
me
try
7-7
Sca
le M
od
els
A
sca
le m
od
el
or
a s
ca
le d
ra
win
g i
s an
obje
ct o
r d
raw
ing w
ith
len
gth
s p
rop
ort
ion
al
to t
he o
bje
ct i
t re
pre
sen
ts.
Th
e s
ca
le o
f a m
od
el
or
dra
win
g i
s th
e r
ati
o o
f th
e
len
gth
of
the m
od
el
or
dra
win
g t
o t
he a
ctu
al
len
gth
of
the o
bje
ct b
ein
g m
od
ele
d o
r d
raw
n.
MA
PS
Th
e s
ca
le o
n t
he
ma
p s
ho
wn
is 0
.75
in
ch
es :
6 m
ile
s.
Fin
d t
he
actu
al
dis
tan
ce
fro
m P
ine
ha
m t
o M
en
lo F
ield
s.
Use
a r
ule
r. T
he d
ista
nce
betw
een
Pin
eh
am
an
d
Men
lo F
ield
s is
abou
t 1.2
5 i
nch
es.
Me
tho
d 1
: W
rit
e a
nd
so
lve
a p
ro
po
rti
on
.
Let
x r
ep
rese
nt
the d
ista
nce
betw
een
cit
ies.
0.7
5 i
n.
−
6 m
i
= 1
.25 i
n.
−
x m
i
0.7
5 ·
x =
6 ·
1.2
5
Cro
ss P
rod
uct
s P
rop
ert
y
x =
10
Sim
pli
fy.
Me
tho
d 2
: W
rit
e a
nd
so
lve
an
eq
ua
tio
n.
Let
a =
act
ual
dis
tan
ce a
nd
m =
map
dis
tan
ce
in i
nch
es.
Wri
te t
he s
cale
as
6 m
i −
0.7
5 i
n. ,
wh
ich
is
6 ÷
0.7
5 o
r 8 m
iles
per
inch
.
a =
8 ·
m
Wri
te a
n e
qu
ati
on
.
= 8
· 1
.25
m =
1.2
5 i
n.
= 1
0
Solv
e.
Th
e d
ista
nce
betw
een
Pin
eh
am
an
d M
en
lo F
ield
s is
10 m
iles.
Exam
ple
ma
p
act
ual
Exerc
ises
Use
th
e m
ap
ab
ov
e a
nd
a c
usto
ma
ry
ru
ler t
o f
ind
th
e a
ctu
al
dis
tan
ce
be
twe
en
ea
ch
pa
ir o
f cit
ies.
Me
asu
re
to
th
e n
ea
re
st
six
tee
nth
of
an
in
ch
.
1
. E
ast
wic
h a
nd
Need
ham
Beach
13 m
iles
2
. N
ort
h P
ark
an
d M
en
lo F
ield
s 18 m
iles
3
. N
ort
h P
ark
an
d E
ast
wic
h 8 m
iles
4
. D
en
vil
le a
nd
Pin
eh
am
4 m
iles
5
. P
ineh
am
an
d E
ast
wic
h 13 m
iles
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Scale
Dra
win
gs a
nd
Mo
dels
Denvill
e Pin
eham
Eastw
ich
Nort
h P
ark
Needham
B
each
Menlo
Fie
lds
0.7
5 in.
6 m
i.
Answers (Lesson 7-6 and Lesson 7-7)
Chapter 7 A20 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
44
G
len
co
e G
eo
me
try
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Scale
Dra
win
gs a
nd
Mo
dels
7-7
Use
Sca
le F
acto
rs
Th
e s
ca
le f
acto
r o
f a d
raw
ing o
r sc
ale
mod
el
is t
he s
cale
wri
tten
as
a u
nit
less
rati
o i
n s
imp
lest
form
. S
cale
fact
ors
are
alw
ays
wri
tten
so t
hat
the m
od
el
len
gth
in
th
e r
ati
o c
om
es
firs
t.
SC
ALE
MO
DE
L A
do
ll h
ou
se
th
at
is 1
5 i
nch
es t
all
is a
sca
le m
od
el
of
a r
ea
l h
ou
se
wit
h a
he
igh
t o
f 2
0 f
ee
t.
a.
Wh
at
is t
he
sca
le o
f th
e m
od
el?
To f
ind
th
e s
cale
, w
rite
th
e r
ati
o o
f a m
od
el
len
gth
to a
n a
ctu
al
len
gth
.
m
od
el
len
gth
−
act
ual
len
gth
=
15 i
n.
−
20 f
t or
3 i
n.
−
4 f
t
Th
e s
cale
of
the m
od
el
is 3
in
.:4 f
t
b.
Ho
w m
an
y t
ime
s a
s t
all
as t
he
actu
al
ho
use
is t
he
mo
de
l?
Mu
ltip
ly t
he s
cale
fact
or
of
the m
od
el
by a
con
vers
ion
fact
or
that
rela
tes
inch
es
to f
eet
to
obta
in a
un
itle
ss r
ati
o.
3 i
n.
−
4 f
t =
3 i
n.
−
4 f
t ·
1 f
t
−
12 i
n. =
3
−
48 o
r 1
−
16
Th
e s
cale
fact
or
is 1
:16.
Th
at
is,
the m
od
el
is
1
−
16 a
s ta
ll a
s th
e a
ctu
al
hou
se.
Exerc
ises
1
. M
OD
EL T
RA
IN T
he l
en
gth
of
a m
od
el
train
is
18 i
nch
es.
It
is a
sca
le m
od
el
of
a t
rain
that
is 4
8 f
eet
lon
g.
Fin
d t
he s
cale
fact
or.
1:3
2
2
. A
RT
A
n a
rtis
t in
Port
lan
d,
Ore
gon
, m
ak
es
bro
nze s
culp
ture
s of
dogs.
Th
e r
ati
o o
f th
e
heig
ht
of
a s
culp
ture
to t
he a
ctu
al
heig
ht
of
the d
og i
s 2:3
. If
th
e h
eig
ht
of
the s
culp
ture
is
14 i
nch
es,
fin
d t
he h
eig
ht
of
the d
og.
21 i
n.
3
. B
RID
GE
S T
he s
pan
of
the B
en
jam
in F
ran
kli
n s
usp
en
sion
bri
dge i
n P
hil
ad
elp
hia
, P
en
nsy
lvan
ia,
is 1
750 f
eet.
A m
od
el
of
the b
rid
ge h
as
a s
pan
of
42 i
nch
es.
Wh
at
is t
he
rati
o o
f th
e s
pan
of
the m
od
el
to t
he s
pan
of
the a
ctu
al
Ben
jam
in F
ran
kli
n B
rid
ge?
1− 5
00
Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-7
Ch
ap
ter
7
45
G
len
co
e G
eo
me
try
7-7
MA
PS
U
se
th
e m
ap
sh
ow
n a
nd
a
cu
sto
ma
ry
ru
ler t
o f
ind
th
e a
ctu
al
dis
tan
ce
be
twe
en
ea
ch
pa
ir o
f cit
ies.
Me
asu
re
to
th
e n
ea
re
st
six
tee
nth
of
an
in
ch
.
1
. P
ort
Jaco
b a
nd
Sou
thp
ort
2
. P
ort
Jaco
b a
nd
Bri
gh
ton
Beach
3
. B
righ
ton
Beach
an
d P
irate
s’ C
ove
4
. E
ast
port
an
d S
an
d D
oll
ar
Reef
5
. S
CA
LE
MO
DE
L S
an
jay i
s m
ak
ing a
139 c
en
tim
ete
rs l
on
g s
cale
mod
el
of
the P
art
hen
on
for
his
Worl
d H
isto
ry c
lass
. T
he a
ctu
al
len
gth
of
the P
art
hen
on
is
69.5
mete
rs l
on
g.
a.
Wh
at
is t
he s
cale
of
the m
od
el?
b.
How
man
y t
imes
as
lon
g a
s th
e a
ctu
al
Part
hen
on
is
the m
od
el?
6
. A
RC
HIT
EC
TU
RE
A
n a
rch
itect
is
mak
ing a
sca
le m
od
el
of
an
off
ice b
uil
din
g h
e w
ish
es
to
con
stru
ct.
Th
e m
od
el
is 9
in
ches
tall
. T
he a
ctu
al
off
ice b
uil
din
g h
e p
lan
s to
con
stru
ct w
ill
be 7
5 f
eet
tall
.
a.
Wh
at
is t
he s
cale
of
the m
od
el?
b.
Wh
at
scale
fact
or
did
th
e a
rch
itect
use
to b
uil
d h
is m
od
el?
7. W
HIT
E H
OU
SE
C
raig
is
mak
ing a
sca
le d
raw
ing o
f th
e W
hit
e H
ou
se o
n a
n
8.5
-by-1
1-i
nch
sh
eet
of
pap
er.
Th
e W
hit
e H
ou
se i
s 168 f
eet
lon
g a
nd
152 f
eet
wid
e.
Ch
oose
an
ap
pro
pri
ate
sca
le f
or
the d
raw
ing a
nd
use
th
at
scale
to d
ete
rmin
e t
he
dra
win
g’s
dim
en
sion
s.
8
. G
EO
GR
AP
HY
C
hoose
an
ap
pro
pri
ate
sca
le a
nd
con
stru
ct a
sca
le d
raw
ing o
f each
rect
an
gu
lar
state
to f
it o
n a
3-b
y-5
-in
ch i
nd
ex c
ard
.
a. T
he s
tate
of
Colo
rad
o i
s ap
pro
xim
ate
ly 3
80 m
iles
lon
g (
east
to w
est
) an
d 2
80 m
iles
wid
e (
nort
h t
o s
ou
th).
b.
Th
e s
tate
of
Wyom
ing i
s ap
pro
xim
ate
ly 3
65 m
iles
lon
g (
east
to w
est
) an
d 2
65 m
iles
wid
e (
nort
h t
o s
ou
th).
Sk
ills
Pra
ctic
e
Scale
Dra
win
gs a
nd
Mo
dels
52 1
−
2 m
i
72 1
−
2 m
i
50 m
i
77 1
−
2 m
i
Port
Jacob Eastp
ort
Brighto
n B
each
Pirate
s’ C
ove
South
port
Sand D
olla
r R
eef
0.5
in.
20 m
i
1
−
500
2 c
m:1
m
3 i
n.:
25 f
t
1:1
00
1 i
n.:
18 f
t; 8
4
−
9 i
n.
× 9
1
−
3 i
n.
1 i
n.:
80 m
i; d
raw
ing
sh
ou
ld b
e a
bo
ut
4.7
5 i
n.
× 3
.5 i
n.
1 i
n.:
75 m
i; d
raw
ing
sh
ou
ld b
e a
bo
ut
4.8
7 i
n.
× 3
.53 i
n.
Answers (Lesson 7-7)
Chapter 7 A21 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
46
G
len
co
e G
eo
me
try
Practi
ce
Scale
Dra
win
gs a
nd
Mo
dels
7-7
MA
PS
U
se
th
e m
ap
of
Ce
ntr
al
Ne
w J
erse
y s
ho
wn
an
d a
n i
nch
ru
ler t
o f
ind
th
e
actu
al
dis
tan
ce
be
twe
en
ea
ch
pa
ir o
f cit
ies.
Me
asu
re
to
th
e n
ea
re
st
six
tee
nth
of
an
in
ch
.
1
. H
igh
lan
d P
ark
an
d M
etu
chen
ab
ou
t 4.4
65 m
iles
2
. N
ew
Bru
nsw
ick
an
d R
obin
vale
ab
ou
t 6.1
1 m
iles
3
. R
utg
ers
Un
ivers
ity L
ivin
gst
on
Cam
pu
s an
d R
utg
ers
Un
ivers
ity
Cook
–D
ou
gla
ss C
am
pu
s
ab
ou
t 3.4
075 m
iles
4
. A
IRP
LA
NE
S W
illi
am
is
bu
ild
ing a
scale
mod
el
of
a B
oein
g 7
47–400 a
ircr
aft
.
Th
e w
ingsp
an
of
the m
od
el
is a
pp
roxim
ate
ly 8
feet
10
1 − 16
in
ches.
If
the s
cale
fact
or
of
the
mod
el
is a
pp
roxim
ate
ly 1
:24,
wh
at
is t
he a
ctu
al
win
gsp
an
of
a B
oein
g 7
47–400 a
ircr
aft
?
212.1
25 f
eet
5
. E
NG
INE
ER
ING
A
civ
il e
ngin
eer
is m
ak
ing a
sca
le m
od
el
of
a h
igh
way o
n r
am
p.
Th
e l
en
gth
of
the m
od
el
is 4
in
ches
lon
g.
Th
e a
ctu
al
len
gth
of
the o
n r
am
p i
s 500 f
eet.
a.
Wh
at
is t
he s
cale
of
the m
od
el?
1 i
n.:
125 f
t
b.
How
man
y t
imes
as
lon
g a
s th
e a
ctu
al
on
ram
p i
s th
e m
od
el?
1500
c.
How
man
y t
imes
as
lon
g a
s th
e m
od
el
is t
he a
ctu
al
on
ram
p?
500
6
. M
OV
IES
A
movie
dir
ect
or
is c
reati
ng a
sca
le m
od
el
of
the E
mp
ire S
tate
Bu
ild
ing t
o
use
in
a s
cen
e.
Th
e E
mp
ire S
tate
Bu
ild
ing i
s 1250 f
eet
tall
.
a.
If t
he m
od
el
is 7
5 i
nch
es
tall
, w
hat
is t
he s
cale
of
the m
od
el?
3 i
n.:
50 f
t
b.
How
tall
wou
ld t
he m
od
el
be i
f th
e d
irect
or
use
s a s
cale
fact
or
of
1:7
5?
16 f
eet
8 i
nch
es
7
. M
ON
A L
ISA
A
vis
itor
to t
he L
ou
vre
Mu
seu
m i
n P
ari
s w
an
ts t
o s
ketc
h a
dra
win
g
of
the M
on
a L
isa
, a f
am
ou
s p
ain
tin
g.
Th
e o
rigin
al
pain
tin
g i
s 77 c
en
tim
ete
rs b
y
53 c
en
tim
ete
rs.
Ch
oose
an
ap
pro
pri
ate
sca
le f
or
the r
ep
lica
so t
hat
it w
ill
fit
on
a
8.5
-by-1
1-i
nch
sh
eet
of
pap
er.
1 i
n.:
7 c
m
1 in.
1.8
8 m
i
Hig
hla
nd
Pa
rk
Me
tuch
en
Ne
wB
run
sw
ick
Ro
bin
va
le
Ru
tge
rsU
niv
-Co
ok-D
ou
gla
ss
Ca
mp
us
Ru
tge
rsU
niv
-Liv
ing
sto
nC
am
pu
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-7
Ch
ap
ter
7
47
G
len
co
e G
eo
me
try
7-7
1
. M
OD
ELS
L
uk
e w
an
ts t
o m
ak
e a
sca
le
mod
el
of
a B
oein
g 7
47 j
etl
iner.
He w
an
ts
every
foot
of
his
mod
el
to r
ep
rese
nt
50 f
eet.
Com
ple
te t
he f
oll
ow
ing t
able
.
Pa
rt
Ac
tua
l
len
gth
(in
.)
Mo
de
l
len
gth
(in
.)
Win
g S
pa
n2
53
7
50.7
4
Le
ng
th2
78
2
55.6
4
Ta
il H
eig
ht
39
2
7.8
4(S
ou
rce:
Boein
g)
2
. P
HO
TO
GR
AP
HS
T
racy
is
4 f
eet
tall
an
d
her
fath
er
is 6
feet
tall
. In
a p
hoto
gra
ph
of
the t
wo o
f th
em
sta
nd
ing s
ide b
y s
ide,
Tra
cy’s
im
age i
s 2 i
nch
es
tall
.
6 ft
4 ft
Alt
hou
gh
th
eir
im
ages
are
mu
ch
small
er,
th
e r
ati
o o
f th
eir
heig
hts
rem
ain
s th
e s
am
e.
How
tall
is
Tra
cy’s
fath
er’
s im
age i
n t
he p
hoto
? W
hat
is
the s
cale
of
the p
hoto
?
1:2
4
3
. T
OW
ER
S T
he T
ok
yo T
ow
er
in J
ap
an
is
curr
en
tly t
he w
orl
d’s
tall
est
self
-
sup
port
ing s
teel
tow
er.
It
is 3
33 m
ete
rs
tall
.
a.
Heero
bu
ild
s a m
od
el
of
the T
ok
yo
Tow
er
that
is 2
775 m
illi
mete
rs t
all
.
Wh
at
is t
he s
cale
of
Heero
’s m
od
el?
25 m
m:3
m
b.
How
man
y t
imes
as
tall
as
the a
ctu
al
tow
er
is t
he m
od
el?
4
. P
UP
PIE
S M
ere
dit
h’s
new
Pom
era
nia
n
pu
pp
y i
s 7 i
nch
es
tall
an
d 9
in
ches
lon
g.
Sh
e w
an
ts t
o m
ak
e a
dra
win
g o
f h
er
new
Pom
era
nia
n t
o p
ut
in h
er
lock
er.
If
the
sheet
of
pap
er
she i
s u
sin
g i
s 3 i
nch
es
by
5 i
nch
es,
fin
d a
n a
pp
rop
riate
sca
le f
act
or
for
Mere
dit
h t
o u
se i
n h
er
dra
win
g.
1:2
.5 o
r 2:5
(an
sw
ers
may v
ary
, b
ut
sh
ou
ld b
e a
t le
ast
gre
ate
r th
an
1:2
.34)
5
. M
AP
SC
arl
os
mak
es
a m
ap
of
his
neig
hborh
ood
for
a p
rese
nta
tion
. T
he
scale
of
his
map
is
1 i
nch
:125 f
eet.
a.
How
man
y f
eet
do 4
in
ches
rep
rese
nt
on
th
e m
ap
?
500 f
t
b.
Carl
os
lives
250 f
eet
aw
ay f
rom
An
dre
w.
How
man
y i
nch
es
sep
ara
te
Carl
os’
hom
e f
rom
An
dre
w’s
on
the m
ap
?2 i
n.
c.
Du
rin
g a
pra
ctic
e r
un
in
fro
nt
of
his
pare
nts
, C
arl
os
reali
zes
that
his
map
is f
ar
too s
mall
. H
e d
eci
des
to m
ak
e
his
map
5 t
imes
as
larg
e.
Wh
at
wou
ld
be t
he s
cale
of
the l
arg
er
map
?
1 i
n.:
25 f
t
Wo
rd
Pro
ble
m P
racti
ce
Scale
Dra
win
gs a
nd
Mo
dels
1
−
12
0
Answers (Lesson 7-7)
Chapter 7 A22 Glencoe Geometry
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
48
G
len
co
e G
eo
me
try
7-7
Are
a a
nd
Vo
lum
e o
f S
cale
Mo
dels
an
d D
raw
ing
s
You
have a
lread
y l
earn
ed
abou
t ch
an
ges
of
len
gth
measu
res
betw
een
sca
le m
od
els
an
d t
he
obje
ct t
hat
is b
ein
g m
od
ele
d.
Th
e a
reas
an
d v
olu
mes
of
scale
mod
els
an
d d
raw
ings
als
o
chan
ge,
bu
t by m
ult
iple
s d
iffe
ren
t th
an
th
e “
scale
fact
or.
”
Y
ua
n i
s m
ak
ing
a s
ca
le m
od
el
of
a c
yli
nd
er.
Th
e a
ctu
al
cy
lin
de
r h
as
a r
ad
ius o
f r i
nch
es a
nd
a h
eig
ht
of h
in
ch
es.
Th
e s
ca
le f
acto
r o
f th
e m
od
el
is 1
:2.
Wh
at
is t
he
ra
tio
of
vo
lum
es o
f th
e m
od
el
cy
lin
de
r t
o t
he
actu
al
cy
lin
de
r?
Th
e v
olu
me f
orm
ula
for
a c
yli
nd
er
is V
= π
r2h
. T
he a
ctu
al
cyli
nd
er’
s volu
me i
s π
r2h
.
If t
he c
yli
nd
er
is s
cale
d d
ow
n b
y a
fact
or
of
1:2
, th
e n
ew
rad
ius
wil
l be 1
−
2 r
an
d t
he n
ew
heig
ht
wil
l be 1
−
2 h
.
V =
π ( 1
−
2 r
) 2
( 1
−
2 h
)
= 1
−
8 π
r2h
Th
e m
od
el’s
volu
me i
s 1
−
8 o
f th
e a
ctu
al
volu
me.
Exerc
ises
1
. C
on
sid
er
a p
ain
tin
g o
n a
22-i
nch
-by-2
8-i
nch
can
vas.
Su
pp
ose
you
wis
h t
o m
ak
e a
1:2
sc
ale
mod
el
of
the p
ain
tin
g f
or
art
cla
ss.
Wh
at
is t
he r
ati
o o
f are
as
of
the m
od
el
pain
tin
g
to t
he a
ctu
al
pain
tin
g?
(Are
a =
Len
gth
× W
idth
) 1
−
4
2
. T
he P
ark
s an
d R
ecr
eati
on
Off
ice i
s p
lan
nin
g a
new
cir
cula
r p
laygro
un
d w
ith
a r
ad
ius
of
30 f
eet.
Befo
re t
hey c
an
con
stru
ct t
he p
laygro
un
d,
they a
sk a
n a
rch
itect
to c
reate
a 1
:20
scale
mod
el
of
the p
rop
ose
d p
laygro
un
d s
uch
th
at
the n
ew
rad
ius
is 1
.5 f
eet.
Wh
at
is t
he
rati
o o
f are
as
of
the m
od
el
pla
ygro
un
d t
o t
he p
rop
ose
d a
ctu
al
pla
ygro
un
d?
(Are
a =
π ×
(ra
diu
s)2)
1
−
40
0
3
. A
refr
igera
tor
man
ufa
ctu
rer
use
s a 7
-foot-
by-3
-foot-
by-3
-foot
box f
or
its
stan
dard
mod
el.
T
he m
ark
eti
ng t
eam
su
ggest
s th
e m
an
ufa
ctu
rer
start
sell
ing a
sm
all
er,
low
er-
pri
ced
re
frig
era
tor
wit
h a
sca
le f
act
or
of
4:5
to t
he s
tan
dard
mod
el.
If
the b
ox i
s re
du
ced
by a
si
mil
ar
scale
, w
hat
is t
he r
ati
o o
f volu
mes
of
the n
ew
, sm
all
er
box t
o t
he c
urr
en
t box?
(Volu
me =
len
gth
× w
idth
× h
eig
ht)
6
4
−
12
5
4
. C
on
sid
er
a c
ube w
ith
sid
e l
en
gth
s x.
If e
ach
sid
e o
f th
e c
ube i
s sc
ale
d b
y a
fact
or
of
1:y
, w
hat
is t
he r
ati
o o
f volu
mes
of
the m
od
el
cube t
o t
he a
ctu
al
cube?
(Volu
me =
len
gth
× w
idth
× h
eig
ht)
( 1
−
y ) 3
En
ric
hm
en
t
Exam
ple
Answers (Lesson 7-7)
Chapter 7 A23 Glencoe Geometry
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Chapter 7 A24 Glencoe Geometry
Chapter 7 Assessment Answer KeyQuiz 1 (Lessons 7-1 and 7-2) Quiz 3 (Lessons 7-5 and 7-6) Mid-Chapter Test
Page 51 Page 52 Page 53
Quiz 2 (Lessons 7-3 and 7- 4) Quiz 4 (Lesson 7-7)
Page 51 Page 52
1.
2.
3.
4.
5.
20, 65, 95
276 students
△BAC ∼ △QPR or △ABC ∼ △QPR by
SAS.
x = 4; scale factor 5:4
B
1.
2.
3.
4.
5.
yes; AA
No; the sides are
not proportional.
△ABD ∼ △CDE
or △ADB ∼ △CDF; 8
Not parallel because
JM −
MK ≠ JN
− NL
20
1.
2.
3.
4.
5.
2.3 cm
corresp. altitudes are
proportional to the
corresp. sides
5.3 cm
reduction; 1 −
2
y
x
1.
2.
3.
4.
2:5
33 in.
1:3.5
D
1.
2.
3.
4.
5.
B
J
C
J
B
6.
7.
8.
9.
10.
No; SAS does not apply.
yes; SAS
Not parallel because
JM
− MK
≠ JN
− LN
9
2.9 in.
Answers
Co
pyri
gh
t ©
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nco
e/M
cG
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-Hill, a
div
isio
n o
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he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 7 A25 Glencoe Geometry
Chapter 7 Assessment Answer KeyVocabulary Test Form 1
Page 54 Page 55 Page 56
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ratio
scale factor
midsegment of a triangle
extremes
means
false; similar polygons
false; proportion
true
Sample answer: product of means is equal to product of
extremes
Sample answer: a segment with
endpoints that are the midpoints of any two
sides of a triangle
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
J
B
G
B
J
B
H
A
G
11.
12.
13.
14.
15.
16.
17.
18.
19.
D
J
B
F
B
G
D
H
D
B: 9.6
Co
pyrig
ht ©
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oe
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Gra
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ill, a d
ivis
ion
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Mc
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w-H
ill Co
mp
an
ies, In
c.
Chapter 7 A26 Glencoe Geometry
Chapter 7 Assessment Answer KeyForm 2A Form 2B
Page 57 Page 58 Page 59 Page 60
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
F
D
H
B
H
C
F
C
G
11.
12.
13.
14.
15.
16.
17.
18.
D
J
B
G
C
F
A
J
B: 32
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
H
B
J
B
G
D
G
B
H
11.
12.
13.
14.
15.
16.
17.
18.
D
F
C
J
B
F
D
H
B: 26
Answers
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pyri
gh
t ©
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Mc
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om
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nie
s,
Inc
.
Chapter 7 A27 Glencoe Geometry
Chapter 7 Assessment Answer KeyForm 2C
Page 61 Page 62
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
3:7
Yes; corres. are !.
30 ft
18
42.5 ft
6.3
18.2
72
△PQR ∼ △STR
2 1 − 2
Yes. The right angles
are congruent. The
legs are proportional.
By SAS similarity, the
triangles are similar.
12.
13.
14.
15.
16.
17.
18.
B:
9.5
42
47
2
3
14.4
4
7
Co
pyrig
ht ©
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oe
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Gra
w-H
ill, a d
ivis
ion
of T
he
Mc
Gra
w-H
ill Co
mp
an
ies, In
c.
Chapter 7 A28 Glencoe Geometry
Chapter 7 Assessment Answer KeyForm 2D
Page 63 Page 64
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
5:11
No; the corresponding sides are not proportional.
48 ft
4 −
3
188 1 −
3 ft
5.5
15
75
△XYZ ∼ △XNM
7.5
No. The legs of the
right triangles are
not proportional.
12.
13.
14.
15.
16.
17.
18.
B:
2.2
96
85
9.5
2
5 5 −
8
28
4.8
Answers
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pyri
gh
t ©
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n o
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om
pa
nie
s,
Inc
.
Chapter 7 A29 Glencoe Geometry
Chapter 7 Assessment Answer KeyForm 3
Page 65 Page 66
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
4:3
No; corr. sides are
not proportional.
yes; SAS
30 cm by 7.5 cm
5.85
5
104 in.
82
48
8 −
3
5
12.
13.
14.
15.
16.
17.
18.
B:
11 3 −
7
7.2
8 −
5
60
24 ft
9
25.6
(0, 0), (8, 0), (0, 8)
Co
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ht ©
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/Mc
Gra
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Chapter 7 A30 Glencoe Geometry
Chapter 7 Assessment Answer KeyExtended-Response Test, Page 67
Scoring Rubric
Score General Description Speci! c Criteria
4 Superior
A correct solution that
is supported by well-developed,
accurate explanations
• Shows thorough understanding of the concepts of ratios,
properties of proportions, similar ! gures, similar triangles,
dividing segments into parts, proportional parts of triangles,
corresponding perimeters and altitudes.
• Uses appropriate strategies to solve problems.
• Computations are correct.
• Written explanations are exemplary.
• Figures are accurate and appropriate.
• Goes beyond requirements of some or all problems.
3 Satisfactory
A generally correct solution, but may
contain minor ! aws in reasoning or
computation
• Shows an understanding of the concepts of ratios,
properties of proportions, similar ! gures, similar triangles,
dividing segments into parts, proportional parts of
triangles, corresponding perimeters and altitudes.
• Uses appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are effective.
• Figures are mostly accurate and appropriate.
• Satis" es all requirements of problems.
2 Nearly Satisfactory
A partially correct interpretation and/or
solution to the problem
• Shows an understanding of most of the concepts of ratios,
properties of proportions, similar ! gures, similar triangles,
dividing segments into parts, proportional parts of triangles,
corresponding perimeters and altitudes.
• May not use appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are satisfactory.
• Figures are mostly accurate.
• Satis" es the requirements of most of the problems.
1 Nearly Unsatisfactory
A correct solution with no supporting
evidence or explanation
• Final computation is correct.
• No written explanations or work is shown to substantiate the
" nal computation.
• Figures may be accurate but lack detail or explanation.
• Satis" es minimal requirements of some of the problems.
0 Unsatisfactory
An incorrect solution indicating no
mathematical understanding of the
concept or task, or no solution is given
• Shows little or no understanding of most of the concepts of
ratios, properties of proportions, similar ! gures, similar
triangles, dividing segments into parts, proportional parts
of triangles, corresponding perimeters and altitudes.
• Does not use appropriate strategies to solve problems.
• Computations are incorrect.
• Written explanations are unsatisfactory.
• Figures are inaccurate or inappropriate.
• Does not satisfy requirements of problems.
• No answer may be given.
Answers
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Chapter 7 A31 Glencoe Geometry
Chapter 7 Assessment Answer KeyExtended-Response Test, Page 67
Sample Answers
In addition to the scoring rubric found on page A30, the following sample answers may be used as guidance in evaluating open-ended assessment items.
1. 10
− 6 =
5 −
3 or
10 −
2 =
15 −
3
2a. 3:2:2 (Note: Check to be sure that the sum of any two sides of the triangle is greater than the third side. For example, a ratio of 1:1:2 would not be acceptable.)
2b. 18, 12, 12
2c. 12, 8, 8
3. △ABH ∼ △CDI ∼ △GFI ∼ △ADG ∼ △GDE ∼ △CFE ∼ △AGE by the AA Postulate.
4.
FD
CA
B
1
1
E
4–3
3–4
5. Mark the midpoint of each side of △PQR. Connect these points to form △XYZ. Since each segment of △XYZ is a midsegment of △PQR, its length will be half the corresponding side, and therefore the perimeter will be
half the perimeter of △PQR.
P R
Q
X
Y Z
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Chapter 7 A32 Glencoe Geometry
Chapter 7 Assessment Answer KeyStandardized Test Practice
Page 68 Page 69
1.
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
7. A B C D
A B C D
8. F G H J
9. A B C D
10. F G H J
11. A B C D
12. F G H J
13.
14.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
1 2 8
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
1 6
Answers
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Chapter 7 A33 Glencoe Geometry
Chapter 7 Assessment Answer KeyStandardized Test Practice (continued)
Page 70
15.
16.
17.
18.
19.
20
21a.
21b.
21c.
-3
85.5
11 < x < 53
64.5 cm
congruent; TU = WX = √ "" 40 UV = XY = √ "" 53 VT = YU = √ "" 41
m∠1 = 86.5,
m∠2 = 93.5
ST = 6.32, PR = 28.46
slope of −− ST = 1 −
3 ,
slope of −− PR = -3
perpendicular