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Holt McDougal Florida
Larson Geometry
Lesson Transparencies
LAH_GE_11_FL_LT_FM.indd iLAH_GE_11_FL_LT_FM.indd i 11/13/09 10:52:54 AM11/13/09 10:52:54 AM
Copyright © Holt McDougal, a division of Houghton Mifflin Harcourt Publishing Company.
All rights reserved.
Warning: No part of this work may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopying and recording, or by any information storage
or retrieval system without the prior written permission of Holt McDougal unless such copying
is expressly permitted by federal copyright law.
Teachers using HOLT McDOUGAL FLORIDA LARSON GEOMETRY may photocopy complete
pages in sufficient quantities for classroom use only and not for resale.
HOLT McDOUGAL is a trademark of Houghton Mifflin Harcourt Publishing Company.
Printed in the United States of America
If you have received these materials as examination copies free of charge, Holt McDougal
retains title to the materials and they may not be resold. Resale of examination copies is
strictly prohibited.
Possession of this publication in print format does not entitle users to convert this publication,
or any portion of it, into electronic format.
ISBN 13: 978-0-547-24235-4ISBN 10: 0-547-24235-2
1 2 3 4 5 6 7 8 9 XXX 15 14 13 12 11 10 09
LAH_GE_11_FL_LT_FM.indd iiLAH_GE_11_FL_LT_FM.indd ii 11/13/09 10:52:37 AM11/13/09 10:52:37 AM
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iiiGeometry
Lesson Transparencies
ContentsChapter 1 Essentials of Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2 Reasoning and Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter 3 Parallel and Perpendicular Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 4 Congruent Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 5 Relationships Within Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Chapter 6 Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter 7 Right Triangles and Trigonometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Chapter 8 Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter 9 Properties of Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Chapter 10 Properties of Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Chapter 11 Measuring Length and Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Chapter 12 Surface Area and Volume of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
LAH_GE_11_FL_LT_FM.indd iiiLAH_GE_11_FL_LT_FM.indd iii 11/13/09 10:34:52 AM11/13/09 10:34:52 AM
LAH_GE_11_FL_LT_FM.indd ivLAH_GE_11_FL_LT_FM.indd iv 2/27/09 12:54:56 PM2/27/09 12:54:56 PM
Graph each inequality.
1. x ≤ 1 2. 22 ≤ x ≤ 3
3. Juan has more than 5 but fewer than 11 fi sh in his aquarium. Write an inequality to express the number of fi sh f Juan has.
Warm-Ups: 1. 0 2 42224
2. 0 2 42224
3. 5 < f < 11
ANSWERS
Warm-Up ExercisesLESSON
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1Geometry
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LAH_GE_11_FL_LT_CH01.indd 1LAH_GE_11_FL_LT_CH01.indd 1 2/25/09 11:57:50 PM2/25/09 11:57:50 PM
1. Solve 3x 1 5 1 2x 2 4 5 36.
2. Find three cities on this map that appear to be collinear.
ChicagoRockford
BloomingtonQuincy
Springfield
Cairo
Lesson QuizFor use after Lesson 1.1
Use this fi gure for Exercises 1–4.
S
DB
F
A
C
E
1. Give two other names for ‹ ] › AE .
2. Give another name for plane S.
3. Name three collinear points.
4. Name the intersection of ‹ ] › AC
and plane S.
Warm-Ups: 1. 7 2. Chicago, Bloomington, Springfi eld
Lesson Quiz: 1. ‹ ] › EC , ‹ ] › AC 2. plane DEF or EBF
3. A, E, C or D, E, B 4. E
ANSWERS
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Warm-Up ExercisesLESSON
1.2
2 Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH01.indd 2LAH_GE_11_FL_LT_CH01.indd 2 2/25/09 11:57:51 PM2/25/09 11:57:51 PM
1. Find a point between A(23, 5) and B(7, 5).
2. Find the average of 211 and 5.
3. Solve x 1 7
} 2 5 5.
4. Find Ï}
30 to the nearest hundredth.
5. Find Ï}
5 1 Ï}
20 to the nearest hundredth.
Lesson QuizFor use after Lesson 1.2
1. Measure } AB to the nearest 1 }
8 inch.
in. 1
A B
2. Find CE.
C D
7 15
E
3. Plot the points F(23, 5), G(2, 5), H(3, 1), and J(3, 23) in a coordinate plane. Are } FG and } HJ congruent? Explain.
4. Find KL.
0 2 42224
LK
Warm-Ups: 1. Sample: (2, 5) 2. 23 3. 3 4. 5.48 5. 6.71
Lesson Quiz: 1. 1 3 }
8 in. 2. 22
3. No, FG 5 5 and HJ 5 4. 4. 7
ANSWERS
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Warm-Up ExercisesLESSON
1.3
3Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH01.indd 3LAH_GE_11_FL_LT_CH01.indd 3 2/25/09 11:57:52 PM2/25/09 11:57:52 PM
Solve each equation.
1. 5x 1 6 1 2x 2 14 5 90
2. 4x 2 30 1 x 1 25 5 180
3. x }
3 1 2 5 x 2 5
Lesson QuizFor use after Lesson 1.3
1. } AB bisects } CD at E. If CE 5 2 1 }
4 in., fi nd CD.
2. Point M is the midpoint of } XY . Find XM.
X M Y
2x 1 7 8x 2 23
3. Point M is the midpoint of } PQ with endpoints P(2, 26) and Q(28, 0). Find the coordinates of M.
4. The midpoint of } GH is M(4, 21). One endpoint is G(5, 3). Find the coordinates of H.
5. To fi nd the distance between the swing and the sandbox in his backyard, Darren made a graph and found the coordinates of the swing to be (7, 2) and the coordinates of the sandbox to be (23, 8). Find the distance between the swing and the sandbox to the nearest tenth of a unit.
Warm-Ups: 1. 14 2. 37 3. 10.5
Lesson Quiz: 1. 4 1 }
2 in. 2. 17 3. (23, 23)
4. (3, 25) 5. 11.7
ANSWERS
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Warm-Up ExercisesLESSON
1.4
4Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH01.indd 4LAH_GE_11_FL_LT_CH01.indd 4 2/25/09 11:57:54 PM2/25/09 11:57:54 PM
1. The sum of two numbers is 90 and one number is 4 times the other. Write an equation and solve to fi nd the numbers.
2. Find m∠ABD. What kind of angle is it?
1688
128
D
C
A B
Lesson QuizFor use after Lesson 1.4
Classify each angle as acute, obtuse, right, or straight.
1. m∠A 5 908
2. m∠B 5 628
3. m∠C 5 1198
4. If m∠DEG 5 848, fi nd m∠FEG.
E
D
F
G
(x 2 6)8
(3x 1 10)8
5. If ]
› XY bisects ∠ZXW and m∠ZXY 5 368, fi nd m∠ZXW.
Warm-Ups: 1. x 1 4x 5 90; 18, 72 2. 1808, straight
Lesson Quiz: 1. right 2. acute 3. obtuse
4. 148 5. 728
ANSWERS
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Warm-Up ExercisesLESSON
1.5
5Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH01.indd 5LAH_GE_11_FL_LT_CH01.indd 5 2/25/09 11:57:57 PM2/25/09 11:57:57 PM
1. Draw an acute angle and shade the interior.
2. Find the measure of the supplement of a 1308 angle.
3. Find the measure of the complement of an 868 angle.
Lesson QuizFor use after Lesson 1.5
1. ∠1 and ∠2 are supplementary. If m∠1 5 978, fi nd m∠2.
2. ∠3 and ∠4 are complementary angles. If m∠3 5 748, fi nd m∠4.
3. Find m∠EFH. 4. Find m∠ABC.
GE F
H
(3x 2 6)8 (2x 1 16)8
D
C
B
A
(x 1 9)8
(2x)8
5. Is it possible to draw a fi gure that contains exactly one pair of vertical angles? Explain.
Warm-Ups: 1. 2. 508 3. 48
Lesson Quiz: 1. 838 2. 168 3. 968 4. 3685. No; once you have drawn a pair of vertical angles, you have drawn two pairs of opposite rays. This automatically gives another pair of vertical angles.
ANSWERS
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Warm-Up ExercisesLESSON
1.6
6Warm-Up TransparenciesGeometry
LAH_GE_11_FL_LT_CH01.indd 6LAH_GE_11_FL_LT_CH01.indd 6 2/25/09 11:57:58 PM2/25/09 11:57:58 PM
1. Find the approximate distance between (2, 3) and (21, 4). Round to the nearest tenth.
2. Change 72 inches to feet.
3. Solve 1 }
2 (5x) 5 30.
4. Michelle will put braid around the edges of a rug. She calculates that she needs 14 yards. How many feet of braid does she need?
Lesson QuizFor use after Lesson 1.6
1. Draw a convex hexagon.
2. This fi gure shows the tiles on a kitchen fl oor. What type of polygon are the tiles? Are they regular polygons?
3. This fi gure is a regular polygon. Find the length of each side.
(x2 1 6x) cm
(x2 2 10x 1 32) cm
Warm-Ups: 1. 3.2 2. 6 ft 3. 12 4. 42 ft
Lesson Quiz: 1.
2. quadrilaterals; not regular 3. 16 cm
ANSWERS
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Warm-Up ExercisesLESSON
1.7
7Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH01.indd 7LAH_GE_11_FL_LT_CH01.indd 7 11/11/09 11:33:12 AM11/11/09 11:33:12 AM
Find the perimeter and area of each fi gure.
1.
4 m
7 m
2. 13 in.
5 in.
12 in.
3. Find the approximate circumference and area of a circle with radius 5 cm.
4. The area of a square game board is 144 in.2. Find the length of a side.
Lesson Quiz: 1. 22 m, 28 m2 2. 30 in., 30 in.2
3. 31.4 cm, 78.5 cm2 4. 12 in.
ANSWERS
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LESSON
1.7 Lesson QuizFor use after Lesson 1.7
GeometryWarm-Up Transparencies 8
LAH_GE_11_FL_LT_CH01.indd 8LAH_GE_11_FL_LT_CH01.indd 8 11/9/09 1:29:49 PM11/9/09 1:29:49 PM
1. Find the length of a segment with endpoints A(1, �3) and B(�2, �7).
2. If M(4, �3) is the midpoint of � RS , and the coordinates of R are (8, �2), fi nd the coordinates of S.
3. ∠A and ∠B are supplementary. If the measure of ∠A is three times the measure of ∠B, fi nd the measure of ∠B.
Warm-Ups: 1. 5 2. (0, �4) 3. 45�
ANSWERS
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LAH_GE_11_FL_LT_CH02.indd 9LAH_GE_11_FL_LT_CH02.indd 9 2/26/09 12:16:28 AM2/26/09 12:16:28 AM
Classify each of the following angles as acute, right, or obtuse.
1. 102� 2. 37�
3. Find the complement and supplement of ∠XYZ if m∠XYZ � 80�.
4. If XY � YZ, is Y the midpoint of � XZ ? If not, give a counterexample.
Lesson QuizFor use after Lesson 2.1
1. Describe a pattern in the numbers. Write the next number in the pattern. 20, 22, 25, 29, 34, . . ..
2. Find a counterexample for the following conjecture: If the sum of two numbers is positive, then the two numbers must be positive.
3. The scatter plot shows the average
Ho
urs
of
ho
mew
ork
00 2 4 6 8
2
4
8
6
Week number
number of hours of homework done per week by a student during the fi rst 10 weeks of a school term. Make a conjecture that could be true. Explain your reasoning.
Warm-Ups: 1. obtuse 2. acute 3. 10�; 100� 4. No; X, Y, and Z need not be collinear.
Lesson Quiz: 1. Start by adding 2 to 22, then add numbers that suc-cessively increase by 1; 40. 2. Sample: 20 � (�10) � 10 3. Sample answer: The student will do about 11 hours of homework in week 11. The number of hours of homework per week increased steadily during the fi rst 10 weeks.
ANSWERS
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LAH_GE_11_FL_LT_CH02.indd 10LAH_GE_11_FL_LT_CH02.indd 10 2/26/09 12:16:31 AM2/26/09 12:16:31 AM
1. Write the converse, inverse, and contrapositive of “If the measure of an angle is less than 90�, then the angle is acute.”
Lesson QuizFor use after Lesson 2.2
1. For the given statement, write the if-then form, the converse, the inverse, and the contrapositive. Sophomores take driving lessons.
2. Decide if the statement about
CD
A
B
the diagram is true. Explain. �
› BD bisects ∠ABC.
Determine whether the statements are good defi nitions.
3. If two angles are supplementary, then the sum of their measures is 180�.
4. If an angle is obtuse, then its measure is greater than that of an acute angle.
Warm-Ups: 1. Converse: If an angle is acute, then the measure is less than 90�. Inverse: If the measure of an angle is not less than 90�, then the angle is not acute. Contrapositive: If an angle is not acute, then its measure is not less than 90�.
Lesson Quiz: 1. If-then: If you are a sophomore, then you take driv-ing lessons. Converse: If you take driving lessons, then you are a sophomore. Inverse: If you are not a sophomore, then you do not take driving lessons. Contrapositive: If you do not take driving lessons, then you are not a sophomore. 2. Yes; point D is in the interior of ∠ABC and m∠ABD � m∠CBD, so
�
› BD bisects ∠ABC.
3. yes 4. no
ANSWERS
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LAH_GE_11_FL_LT_CH02.indd 11LAH_GE_11_FL_LT_CH02.indd 11 2/26/09 12:16:33 AM2/26/09 12:16:33 AM
State which postulate justifi es each statement.
1. If D is in the interior of ∠ABC, then m∠ABD � m∠DBC � m∠ABC.
2. If M is between X and Y, then XM � MY � XY.
3. Find the length of � MN if N is between M and P, MP � 6x � 2, MN � 4x, and MP � 16.
Lesson QuizFor use after Lesson 2.3
1. Use the Law of Detachment to make a valid conclusion in the true situation. If two angles are complementary, then the sum of their measures is 90�. ∠C and ∠D are complementary.
2. Use the Law of Syllogism to make a valid conclusion in the true situation. If water is at room temperature, then it is a liquid. If water is a liquid, then it is not frozen.
Use the true statements below to determine whether the conclusion is true or false. Explain your reasoning. If Jeanine does her homework, then she goes to the movies. If Joaquin goes to the movies, then he buys popcorn. If Jeanine goes to the movies, then she buys popcorn. Jeanine does her homework.
3. Jeanine buys popcorn.
4. If Jeanine goes to the movies, Joaquin goes to the movies.
Warm-Ups: 1. Angle Addition Postulate 2. Segment Addition Postulate 3. 12
Lesson Quiz: 1. m∠C � m∠D � 90� 2. If water is at room temperature, then it is not frozen. 3. true; the Law of Syllogism 4. False; no laws of logic apply.
ANSWERS
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12 Geometry
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LAH_GE_11_FL_LT_CH02.indd 12LAH_GE_11_FL_LT_CH02.indd 12 2/26/09 12:16:34 AM2/26/09 12:16:34 AM
Solve each equation.
1. 6x � 2 � �3x � 16 2. �4(x � 8) � �16
3. Solve P � 2l � 2w for w.
4. ∠S is the complement of ∠R. If m∠R � 38�, fi nd m∠S. If ∠T is also the complement of ∠R, what is true about m∠S and m∠T?
Lesson QuizFor use after Lesson 2.4
1. Use the diagram to write an example of Postulate 7.
RH
F
nG
mJE
2. Decide whether the statement “Two planes can intersect in exactly one point R” is true or false. If false, give a reason.
Use the diagram to determine
BE
D
FN
M
H
G
A
C
if the statement is true or false.
3. The intersection of planes M and N is points B, E, and H.
4. ‹ � › GH lies in plane M.
5. ∠ABE and ∠HED are vertical angles.
Warm-Ups: 1. �2 2. 12 3. w � P � 2 l
� 2 4. 52�; m∠S � m∠T
Lesson Quiz: 1. Line m intersects line n in point F and no other point. 2. False; Postulate 11 says that if two planes intersect, their intersection is a line. 3. false 4. true 5. false
ANSWERS
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LAH_GE_11_FL_LT_CH02.indd 13LAH_GE_11_FL_LT_CH02.indd 13 2/26/09 12:16:36 AM2/26/09 12:16:36 AM
Use a property of equality to complete the statement.
1. If m∠1 � m∠3, then m∠3 � ? .
2. If AB � CD and CD � TU, then ? .
3. If RS � WX, then ? � AB � ? � AB.
4. If m∠EFG � 28� and m∠GFH � 62�, then ? � 62� � m∠EFG � m∠GFH.
Lesson QuizFor use after Lesson 2.5
Solve. Give a reason for each step.
1. �5x � 18 � 3x � 38 2. �3(x � 5) � 2(x � 10)
Identify the property of equality.
3. If m∠3 � m∠5 and m∠5 � m∠8, then m∠3 � m∠8.
4. If CD � EF, then EF � CD.
Warm-Ups: 1. m∠1 2. AB � TU 3. RS; WX 4. 28�
Lesson Quiz:
1. Equation (Reason) 2. Equation (Reason)
�5x � 18 � 3x � 38 (Given) �3(x � 5) � 2(x � 10) (Given)�8x � 18 � �38 (Subtr. Prop. of Eq.) �3x � 15 � 2x � 20
(Distributive Prop.)�8x � �56 (Subtr. Prop. of Eq.) 15 � 5x � 20
(Addition Prop. of Eq.)x � 7 (Division Prop. of Eq.) �5 � 5x (Subtr. Prop. of Eq.) �1 � x (Division Prop. of Eq.)
3. Transitive Prop. of Eq. 4. Symmetric Prop. of Eq.
ANSWERS
GeometryWarm-Up Transparencies
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LAH_GE_11_FL_LT_CH02.indd 14LAH_GE_11_FL_LT_CH02.indd 14 11/9/09 1:32:42 PM11/9/09 1:32:42 PM
Give a reason for each statement.
1. If m∠1 � 90� and m∠2 � 90�, then m∠1 � m∠2.
2. If � AB ⊥ � BC , then ∠ABC is a right angle.
3. If � FG � � RS , then FG � RS.
Lesson QuizFor use after Lesson 2.6
1. Copy and complete the proof. 2. Use the given information
M HA T
to prove the statement.
GIVEN: MA � TH
21
PROVE: MT � AH
Statements (Reasons) GIVEN: m∠1 � m∠2 � 90�;
1. MA � TH ( ? ) m∠1 � 59�
2. ? (Refl exive Prop. of Eq.) PROVE: m∠2 � 31�
3. MA � AT � AT � TH ( ? )
4. MA � AT � MT; AT � TH � AH ( ? )
5. ? (Substitution Prop. of Eq.)
Warm-Ups: 1. (Transitive Prop. of Eq.) 2. (Def. of perpendicular) 3. (Def. of segment congruence) Lesson Quiz:
1. 1. Given 2. Statements (Reasons)
2. AT � AT 1. m∠1 � m∠2 � 90�; m∠1 � 59� (Given)
3. Addition Prop. of Eq. 2. m∠2 � 90� � m∠1 (Subtraction Prop. of Eq.)
4. Segment Add. Post. 3. m∠2 � 90� � 59� (Substitution Prop. of Eq.)
5. MT � AH 4. m∠2 � 31� (Simplify.)
ANSWERS
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LAH_GE_11_FL_LT_CH02.indd 15LAH_GE_11_FL_LT_CH02.indd 15 2/26/09 12:16:39 AM2/26/09 12:16:39 AM
1. Give the reason for each step.
GIVEN: ∠1 � ∠5 1 23
54
PROVE: ∠1 is supplementary to ∠4.
Statements (Reasons)
1. ∠1 � ∠5
2. m∠1 � m∠5
3. ∠4 and ∠5 are a linear pair.
4. ∠4 and ∠5 are supplementary.
5. m∠4 � m∠5 � 180°
6. m∠4 � m∠1 � 180°
7. ∠1 is supplementary to ∠4.
Lesson Quiz: 1. (Given) 2. (Def. of �) 3. (Def. of linear pair) 4. (Linear Pair Post.) 5. (Def. of supplementary) 6. (Substitution Prop. of Eq.) 7. (Def. of supplementary)
ANSWERS
Lesson QuizFor use after Lesson 2.7
LESSON
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LAH_GE_11_FL_LT_CH02.indd 16LAH_GE_11_FL_LT_CH02.indd 16 11/13/09 5:24:21 PM11/13/09 5:24:21 PM
1. Name the hypothesis and conclusion of the statement, “If an animal fl ies, then it is a bird.”
2. Write the converse, inverse, and contrapositive of the conditional, “If a polygon is regular, then it has congruent sides.”
Lesson QuizFor use after 2.3 Focus On Reasoning
1. Make a truth table for the logical statement ~p r ~q.
2. Let p be “the angle is an acute angle” and let q be “the measure of the angle is less than 90°.” Write the conditional statement p r q in words.
Warm-Ups: 1. hypothesis: an animal fl ies; conclusion: it is a bird 2. Converse: If a polygon has congruent sides, then it is regular. Inverse: If a polygon is not regular, then it does not have congruent sides. Contrapositive: If a polygon does not have congruent sides, then it is not regular.
Lesson Quiz: 1. p q ~p ~q ~p r ~qT T F F TT F F T TF T T F FF F T T T
2. If an angle is acute, then its measure is less than 90°.
ANSWERS
LESSON
2.3 Focus On ReasoningWarm-Up Exercises
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Geometry Warm-Up Transparencies 17
LAH_GE_11_FL_LT_CH02.indd 17LAH_GE_11_FL_LT_CH02.indd 17 11/13/09 5:27:27 PM11/13/09 5:27:27 PM
BA
CD
1. Name a line that does not intersect ‹ ] › AD .
2. What is the intersection of ‹ ] › AD and
‹ ] › DB ?
Warm-Ups: 1. ‹ ] › BC 2. D
ANSWERS
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Warm-Up ExercisesLESSON
3.1
18Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH03.indd 18LAH_GE_11_FL_LT_CH03.indd 18 3/11/09 10:13:45 PM3/11/09 10:13:45 PM
Identify the type of angles.
1014
913
1216
1115
48
37
26
15
1. ∠5, ∠7 2. ∠3, ∠6 3. ∠1, ∠8
Lesson QuizFor use after Lesson 3.1
1. Name the pairs of corresponding angles.
78
34
56
12
2. Name the pairs of alternate interior angles.
3. Name the pairs of consecutive interior angles.
4. The fi gure shows an easel. A B
C D
Does ‹
] ›
AB appear to be parallel,
perpendicular, or skew to ‹ ] › CD ?
Warm-Ups: 1. corresponding 2. alternate interior 3. alternate exterior
Lesson Quiz: 1. ∠1 and ∠3; ∠5 and ∠7; ∠2 and ∠4; ∠6 and ∠8 2. ∠2 and ∠7; ∠3 and ∠6 3. ∠2 and ∠3; ∠6 and ∠7 4. parallel
ANSWERSCopy
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Warm-Up ExercisesLESSON
3.2
19Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH03.indd 19LAH_GE_11_FL_LT_CH03.indd 19 3/11/09 10:38:01 PM3/11/09 10:38:01 PM
1. Find the value of x.
(x 1 20)8
528
2. Write the converse of the following statement. If it is raining, then Josh needs an umbrella.
Lesson QuizFor use after Lesson 3.2
What theorem justifi es each statement?
1. ∠3 > ∠6
2. ∠4 and ∠6 are supplementary. 8
76
5
432
1
3. If m∠2 5 1158, fi nd m∠7.
4. Find the values of x and y.
6x8
(y 1 10)8
308
(2x 1 10)8
5. The fi gure shows a plant trellis. 1
2
If m∠1 5 828, fi nd m∠2.
Warm-Ups: 1. 32 2. If Josh needs an umbrella, then it is raining.
Lesson Quiz: 1. Alt. Interior ? Thm. 2. Consec. Interior ? Thm. 3. 1158 4. 17.5, 35 5. 828
ANSWERS
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Warm-Up ExercisesLESSON
3.3
20Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH03.indd 20LAH_GE_11_FL_LT_CH03.indd 20 3/11/09 10:38:14 PM3/11/09 10:38:14 PM
1. Evaluate a 2 b
} c 2 d
if a 5 5, b 5 2, c 5 1, and d 5 7.
2. Solve x 2 3
} 3 2 4
5 1 } 5 . 3. What is the reciprocal of
2 }
3 ?
4. Julie was thinking of a number. The product of her number and 6 is 21. What was Julie’s number?
Lesson QuizFor use after Lesson 3.3
1. Find the value of x that makes p i q.
(2x 1 43)8
p
q
(3x)8
2. Can you prove a i b? If so, what theorem would you use?
a
b
3. Which lines are parallel?
858 1008
808958
E F
D G
4. In the fi gure, if } HJ i } KL and } KL i } MN , what can you conclude?
M N
K L
H J
What theorem justifi es your conclusion?
Warm-Ups: 1. 2 1 } 2 2.
14 } 5 3.
3 }
2 4. 2
1 } 6
Lesson Quiz: 1. 43 2. Yes; Alternate Interior Angles Converse
3. ‹ ] › EF i
‹ ] › DG 4. } HJ i } MN by Transitive Property of Parallel Lines
ANSWERS
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Warm-Up ExercisesLESSON
3.4
21Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH03.indd 21LAH_GE_11_FL_LT_CH03.indd 21 3/11/09 10:14:07 PM3/11/09 10:14:07 PM
1. If 2x 1 5y 5 220 and x 5 0, what is y?
2. What is the slope of the line containing the points (2, 7) and (3, 210)?
3. Orphelia bought x apples. If each apple costs $.59, write an equation for y, the total cost of x apples.
Lesson QuizFor use after Lesson 3.4
1. Find the slope of the line containing the points (4, 23) and (5, 2).
2. Line k passes through the points (21, 2) and (3, 5). Line n passes through the points (3, 7) and (6, 3). Are lines k and n parallel, perpendicular, or neither?
3. A highway has a grade of 7 percent. For each 200 feet it goes horizontally, how many feet does it rise?
Warm-Ups: 1. 24 2. 217 3. y 5 0.59x
Lesson Quiz: 1. 5 2. perpendicular 3. 14 ft
ANSWERS
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Warm-Up ExercisesLESSON
3.5
22Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH03.indd 22LAH_GE_11_FL_LT_CH03.indd 22 3/11/09 10:38:29 PM3/11/09 10:38:29 PM
1. What is the distance between the points (2, 3) and (5, 7)? 2.
C
D
A B
If m∠DBC 5 908, what is m∠ABD?
Lesson QuizFor use after Lesson 3.5
1. Write an equation of the line that has slope 3 }
4 and y-intercept 21.
2. Write an equation of the line that passes through the point (4, 22) and has slope 3.
3. Write an equation of the line that passes through the point (7, 1) and is parallel to the line with equation x 5 4.
4. Write an equation of the line that passes through the point (7, 1) and is perpendicular to the line with equation 6x 2 3y 5 8.
5. Toni’s puppy weighed 10 pounds when it was 2 months old. It gained 2 pounds a month for 6 months. Write an equation for the puppy’s weight w after m months during this time.
Warm-Ups: 1. 5 2. 908
Lesson Quiz: 1. y 5 3 } 4 x 2 1 2. y 5 3x 2 14
3. x 5 7 4. y 5 2 1 } 2 x 1
9 } 2 5. w 5 2m 1 6
ANSWERS
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Warm-Up ExercisesLESSON
3.6
23Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH03.indd 23LAH_GE_11_FL_LT_CH03.indd 23 3/11/09 10:38:43 PM3/11/09 10:38:43 PM
1. Find m∠3.
3
728
2. How do you know that a and b c
da b
are parallel?
3. Find the distance between the two parallel 2
y
22 x (24, 21)
(0, 4)
(5, 0)
(1, 25)
lines. Round to the nearest tenth.
Lesson Quiz: 1. 188 2. Both are perpendicular to c. 3. 6.4
ANSWERS
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Lesson QuizFor use after Lesson 3.6
LESSON
3.6
GeometryWarm-Up Transparencies 24
LAH_GE_11_FL_LT_CH03.indd 24LAH_GE_11_FL_LT_CH03.indd 24 11/13/09 6:58:26 PM11/13/09 6:58:26 PM
John walks 5 blocks north, 4 blocks east, 2 more blocks north, and 1 more block east.
1. How many blocks north of his starting point is he?
2. How many blocks east is he?
3. How many blocks did he walk?
Lesson QuizFor use after 3.6 Focus On Reasoning
1. Find the taxicab distance between the points (1, 1) and (–2, 4).
2. Draw the taxicab circle with radius 3 and center (2, –3).
Warm-Ups: 1. 7 2. 5 3. 12
Lesson Quiz: 1. 6 2. 1
1 x
y
ANSWERS
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LESSON
3.6 Focus On ReasoningWarm-Up Exercises
25Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH03.indd 25LAH_GE_11_FL_LT_CH03.indd 25 11/13/09 6:58:15 PM11/13/09 6:58:15 PM
Classify each angle as acute, obtuse, or right.
1. 908 2. 728
3. 1168
4. How do you know that ∠1 > ∠2?
2
1
Warm-Ups: 1. right 2. acute 3. obtuse 4. Alt. Int. ? Thm.
ANSWERS
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Warm-Up ExercisesLESSON
4.1
26Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 26LAH_GE_11_FL_LT_CH04.indd 26 11/12/09 3:13:42 PM11/12/09 3:13:42 PM
1. When are two angles congruent?
2. In nABC, if m∠A 5 648 and m∠B 5 718, what is m∠C?
3. What property of angle congruence is illustrated by this statement? If ∠A > ∠B and ∠B > ∠C, then ∠A > ∠C.
Lesson QuizFor use after Lesson 4.1
1. Graph nABC with vertices A(0, 6),
1
x
y
1
A
CB
B(24, 21), and C(4, 21). Classify it by its sides. Then determine if it is a right triangle.
2. Find x. Then classify the triangle
(2x)8508
(3x 1 20)8
by its angles.
3. Find the measure of the exterior
(x 1 72)8
(2x)8
408
G
angle shown.
4. Find x and y.
508x8
y8
328
Warm-Ups: 1. when they have the same measure
2. 458 3. Transitive Property
Lesson Quiz: 1. isosceles; not a right triangle 2. 22; acute 3. 1048 4. 82, 58
ANSWERSCopy
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Warm-Up ExercisesLESSON
4.2
27Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 27LAH_GE_11_FL_LT_CH04.indd 27 11/9/09 1:46:35 PM11/9/09 1:46:35 PM
N O
M
R
P
1. Write a congruence statement.
2. How do you know that ∠N > ∠R?
3. Find x.
(7x 2 50)8
(3x)8
(2x 1 10)8
Lesson QuizFor use after Lesson 4.2
In the diagram, nABC > nDEF. Complete each statement.
1. m∠A 5 ?
A
E
F
CD
B
408
808
2. } FD > ?
3. nEDF > ?
4. Write a congruence statement for the two small triangles.
Z YW
X
Explain your reasoning.
Warm-Ups: 1. nMNO > nPRQ 2. Third ? Thm. 3. 30
Lesson Quiz: 1. 608 2. } CA 3. nBAC
4. nWXZ > nYXZ; The diagram tells us that ∠W > ∠Y and ∠WZX > ∠YZX. ∠WXZ > ∠YXZ by the Third ? Thm. From the diagram } WX > } YX and } WZ > } YZ , and } XZ > } XZ by Refl . Prop. of >
ANSWERS
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Warm-Up ExercisesLESSON
4.3
28Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 28LAH_GE_11_FL_LT_CH04.indd 28 11/12/09 3:13:26 PM11/12/09 3:13:26 PM
Given: } DF bisects } CE , } DC > } DE
Prove: nCDF > nEDF
F
E
C
D
Lesson QuizFor use after Lesson 4.3
1. The vertices of nGHI and nRST are G(22, 5), H(2, 5), I(22, 2), R(29, 8), S(25, 8), and T(29, 5). Is nGHI > nRST ? Explain.
2. Is nABC > nXYZ? Explain.
4
4
5
5
6
6
X
Y
A
BC
Z
Warm-Ups: It is given that } DC > } DE and } DF bisects } CE . } CF > } EF by the def. of bisector. } DF > } DF by the Refl . Prop. of > Segs. So nCDF > nEDF by the SSS > Post.
Lesson Quiz:
1. Yes. GH 5 RS 5 4, HI 5 ST 5 5, and IG 5 TR 5 3. By the SSS > Post., it follows that nGHI > nRST. 2. Yes. By the Seg. Add. Post., } AC > } XZ . Also, } AB > } XY and } BC > } YZ . So nABC > nXYZ by the SSS > Post.
ANSWERS
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Warm-Up ExercisesLESSON
4.4
29Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 29LAH_GE_11_FL_LT_CH04.indd 29 11/9/09 1:47:24 PM11/9/09 1:47:24 PM
Warm-Ups: Yes; HL > Thm.
Lesson Quiz: 1. SAS > Post. 2. HL > Thm.
3. ∠S > ∠Y 4. } ST > } YZ
ANSWERS
Tell whether the pair of triangles is congruent or not and why.
Lesson QuizFor use after Lesson 4.4
Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.
1. nABE, nCBD 2. nFGH, nHJK
D E CA
B
J
H
G F
K
State a third congruence that would
R T
S
X Z
Y
allow you to prove nRST > nXYZ by the SAS Congruence Postulate.
3. } ST > } YZ , } RS > } XY
4. ∠T > ∠Z, } RT > } XZ
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Warm-Up ExercisesLESSON
4.5
30Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 30LAH_GE_11_FL_LT_CH04.indd 30 11/9/09 1:47:50 PM11/9/09 1:47:50 PM
Suppose that nXYZ > nRST. Complete each statement.
1. } XY > ? 2. ∠Z > ?
3. m∠S 5 m∠ ?
4. If ∠A > ∠B, m∠A 5 (2x 1 40)8, and m∠B 5 (3x 2 10)8, fi nd x.
Lesson QuizFor use after Lesson 4.5
Tell whether each pair of triangles is congruent by SAS, ASA, SSS, AAS, or HL. If it is not possible to prove the triangles congruent, write not necessarily congruent.
1. 2.
3. Write a fl ow proof.
A D C
B
Given: } BD bisects ∠ABC, ∠A > ∠CProve: nABD > nCBD
Warm-Ups: 1. } RS 2. ∠T 3. Y 4. 50
Lesson Quiz:
1. ASA 2. not necessarily congruent 3.
∠ABD > ∠CBD
Given
Def. of ∠ Bisector
Given
∠A > ∠C
AAS > Thm.
Reflex. Prop.of > Segs.
nABD > nCBD
BD > BD
BD bisects ∠ABC.
ANSWERS
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Warm-Up ExercisesLESSON
4.6
31Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 31LAH_GE_11_FL_LT_CH04.indd 31 11/9/09 1:48:15 PM11/9/09 1:48:15 PM
Warm-Ups: 1. equilateral 2. isosceles 3. scalene4. 608 5. 778, 778
Lesson Quiz: 1. nAEC > nDEB by the AAS Cong. Thm. or by the ASA Cong. Post. 2. Show } LM > } LM by the Refl . Prop. of > Segs. Hence nOLM > nNML by the SAS Cong. Post. This gives ∠NLM > ∠OML, since Corr. Parts of > ns are >. So∠1 > ∠2 by the Vert. ? Thm. and properties of > ?.
ANSWERS
Classify each triangle by its sides.
1. 2 cm, 2 cm, 2 cm 2. 7 ft, 11 ft, 7 ft
3. 9 m, 8 m, 10 m
4. In nABC, if m∠A 5 708 and m∠B 5 508, what is m∠C ?
5. In nDEF, if m∠D 5 m∠E and m∠F 5 268, what are the
measures of ∠D and ∠E?
Lesson QuizFor use after Lesson 4.6
1. Tell which triangles you can show are congruent in order to prove AE 5 DE. What postulate or theorem would you use?
B D
E
A C
2. Write a plan to prove ∠1 > ∠2. L
NO
2M1
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Warm-Up ExercisesLESSON
4.7
32Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 32LAH_GE_11_FL_LT_CH04.indd 32 11/9/09 1:48:39 PM11/9/09 1:48:39 PM
Warm-Ups: 1. 13 2. (9, 5) 3. Yes, by the SSS Cong. Post. or by the SAS Cong. Post.
Lesson Quiz: 1. 8 2. 3 3. 348, 348 4. 66 cm
ANSWERS
1. Find the length of } AB for A(2, 7) and B(7, 25).
2. What point is 6 units to the right of (3, 5)?
3. Are these triangles congruent?
1
x
y
21
Lesson QuizFor use after Lesson 4.7
Find the value of x.
1.
x
8
2.
7x 1 3
24
19
3. If the measure of the vertex angle of an isosceles triangle is 1128,
what are the measures of the base angles?
4. Find the perimeter of the triangle.
(3x 2 5) cm
(2x 1 4) cm(x 1 13) cm
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Warm-Up ExercisesLESSON
4.8
33Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 33LAH_GE_11_FL_LT_CH04.indd 33 11/9/09 1:49:08 PM11/9/09 1:49:08 PM
1. Use coordinate notation to describe the translation 3 units to the
left and 1 unit up.
2. Use a refl ection in the x-axis to
1
x
y
21
draw the other half of the fi gure.
3. Tell whether } XY is a rotation of } GH about the origin if the points are X(�6, 2), Y(�4, 3), G(6, �2), and H(4, �3). If so, give the angle and direction of rotation.
Lesson Quiz: 1. (x, y) r (x � 3, y � 1)
2.
1
x
y
21
3. Yes; 180� clockwise orcounterclockwise
ANSWERS
LESSON
4.8 Lesson QuizFor use after Lesson 4.8
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34Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH04.indd 34LAH_GE_11_FL_LT_CH04.indd 34 11/9/09 1:49:27 PM11/9/09 1:49:27 PM
In Exercises 1–4, use A(0, 10), B(24, 0), and C(0, 0).
1. Find AB. 2. Find the midpoint of } CA .
3. Find the midpoint of } AB . 4. Find the slope of } AB .
Warm-Ups: 1. 26 2. (0, 5) 3. (12, 5) 4. 2 5 } 12
ANSWERS
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Warm-Up ExercisesLESSON
5.1
35Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH05.indd 35LAH_GE_11_FL_LT_CH05.indd 35 11/11/09 11:50:35 AM11/11/09 11:50:35 AM
1. Solve 3x 5 8x 2 15. 2. Solve 6x 1 3 5 8x 2 14.
3. If M is the midpoint of } AB , AM 5 5x 2 2, and MB 5 3x 1 6, fi nd AB.
Lesson QuizFor use after Lesson 5.1
Use the fi gure below for Exercises 1–4.
1. If UV 5 13, fi nd RT.
2. If ST 5 20, fi nd UW.
R W T
VU
S
3. If the perimeter of nRST 5 68 inches, fi nd the perimeter of nUVW.
4. If VW 5 2x 2 4 and RS 5 3x 2 3, what is VW?
5. Place a rectangle in a coordinate plane so its vertical side has length a and its horizontal side has width 2a. Label the coordinates of each vertex.
Warm-Ups: 1. 3 2. 8.5 3. 36
Lesson Quiz: 1. 26 2. 10 3. 34 in. 4. 65.
x
y
(0, 0)
(0, a)
(2a, 0)
(2a, a)
ANSWERS
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Warm-Up ExercisesLESSON
5.2
36Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH05.indd 36LAH_GE_11_FL_LT_CH05.indd 36 11/9/09 1:52:49 PM11/9/09 1:52:49 PM
1. ]
› AD bisects ∠BAC. Find x.
C
D
B
A
(5x 2 32.5)8
(3x 1 7.5)8
2. Solve x2 1 122 5 169.
3. The legs of a right triangle measure 15 feet and 20 feet. Find the length of the hypotenuse.
Lesson QuizFor use after Lesson 5.2
In Exercises 1 and 2, fi nd AB.
1.
A C
B
4x 2 73x 1 1
2. C
AB 7x
5x 1 7
3. In this diagram, the perpendicular
C
G
E
B
D
FA
7
5bisectors of nABC meet at point G. Find EC and GC.
Warm-Ups: 1. 20 2. 65 3. 25 ft
Lesson Quiz: 1. 25 2. 24.5 3. 5; 7
ANSWERS
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Warm-Up ExercisesLESSON
5.3
37Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH05.indd 37LAH_GE_11_FL_LT_CH05.indd 37 11/9/09 1:53:31 PM11/9/09 1:53:31 PM
1. For A(24, 8) and B(5, 8), fi nd the midpoint of } AB .
2. For A(23, 2) and B(4, 21), fi nd the length of } AB .
3. For A(0, 4) and C(18, 4), fi nd the length of } AB , where B is a
point 2 }
3 the distance from A to C.
Lesson QuizFor use after Lesson 5.3
Find the value of x.
1.
(3x 1 4)8
(4x 2 8)8
2. (4x 1 10)8
3. Point D is the incenter of nXYZ. Find DB.
BD
2624
Z
C
X
A
Y
Warm-Ups: 1. 1 1 } 2 , 8 2 2. Ï
}
58 3. 12
Lesson Quiz: 1. 12 2. 20 3. 10
ANSWERS
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Warm-Up ExercisesLESSON
5.4
38Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH05.indd 38LAH_GE_11_FL_LT_CH05.indd 38 11/9/09 1:54:13 PM11/9/09 1:54:13 PM
1. Solve 3x 1 8 < 29.
2. Solve 15 > 22x 2 9.
3. Solve 2x 2 2 < (3x 2 4) 1 (x 2 8).
4. Find all integer solutions for 4 < x < 11.
5. A triangle has angle measures 828 and 348. Find the measure of the third angle.
Lesson QuizFor use after Lesson 5.4
In Exercises 1–3, use the diagram. G is the centroid of nABC.
E
B
CF
G
A
D 1. If BG 5 9, fi nd BF.
2. If BD 5 12, fi nd AD.
3. If CD 5 27, fi nd GC.
4. Find the centroid of nABC.
1
x
y B
C
A
21
5. Which type of triangle has its orthocenter on the triangle?
Warm-Ups: 1. x < 7 2. x > 212 3. x > 5 4. 5, 6, 7, 8, 9, 10 5. 648
Lesson Quiz: 1. 13.5 2. 12 3. 18 4. (1, 1)5. a right triangle
ANSWERS
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Warm-Up ExercisesLESSON
5.5
39Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH05.indd 39LAH_GE_11_FL_LT_CH05.indd 39 11/9/09 1:54:34 PM11/9/09 1:54:34 PM
1. Write the if-then form, converse, inverse, and contrapositive of the given statement. 3x 2 8 5 22 because x 5 10.
2. In nABC, BC 5 18, AB 5 13, and AC 5 16. List the angles of the triangle from least to greatest.
Lesson QuizFor use after Lesson 5.5
In Exercises 1 and 2, list the sides or angles in order from least to greatest.
1.
508608
708
A C
B 2.
R 30
2546
S
T
Tell whether the side lengths can form a triangle.
3. 37 m, 35 m, 18 m
4. 3 ft, 3 ft, 6 ft
5. Jeremy wants to build a triangular toy using sticks. He has one stick that is 12 inches and another that is 10 inches. What are the possible lengths of the third side of the triangle?
Warm-Ups: 1. If x 5 10, then 3x 2 8 5 22. Con: If 3x 2 8 5 22, then x 5 10. Inv: If x Þ 10, then 3x 2 8 Þ 22. Contra: If 3x 2 8 Þ 22, then x Þ 10. 2. ∠C, ∠B, ∠A
Lesson Quiz: 1. } AB , } BC , } AC 2. ∠R, ∠T, ∠S
3. yes 4. no 5. greater than 2 in. and less than 22 in.
ANSWERS
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Warm-Up ExercisesLESSON
5.6
40Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH05.indd 40LAH_GE_11_FL_LT_CH05.indd 40 11/9/09 1:55:16 PM11/9/09 1:55:16 PM
Complete each statement with < , > , or �.
1. KL ? NP 2. m∠1 ? m∠2
LJ
M
N
P
K
758
808
Y
ZW
X
1222
28
2
128
3. Suppose you want to write an indirect proof of this statement: “In �ABC, if m∠A > 90� then �ABC is not a right triangle.” What temporary assumption should start your proof?
Lesson Quiz: 1. � 2. �
3. Assume �ABC is a right triangle.
ANSWERS
Lesson QuizFor use after Lesson 5.6
LESSON
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41Algebra 1
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH05.indd 41LAH_GE_11_FL_LT_CH05.indd 41 12/8/09 10:55:42 PM12/8/09 10:55:42 PM
1. Simplify 3x2
_ 9x
. 2. Solve 2n � 18 p 32.
3. Solve 4x � 2x � 12. 4. Solve x � ��
36 p 16 .
5. A triangle has angle measures 18� and 82�. Find the measure of the third angle.
Warm-Ups: 1. x �
3 2. 288 3. 6 4. 24 5. 80�
ANSWERS
Warm-Up ExercisesLESSON
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42Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH06.indd 42LAH_GE_11_FL_LT_CH06.indd 42 11/9/09 2:00:48 PM11/9/09 2:00:48 PM
Solve each proportion.
1. 3 �
8 �
6 � x � 1
2. 8 �
3 �
x � 1 � 6
3. 3 � 6 �
8 � x � 1
4. The area of a rectangle is 750 square meters. The ratio of the width to the length is 5 : 6. Find the width and the length.
Lesson QuizFor use after Lesson 6.1
1. Simplify the ratio 1200 cm : 1.8 m.
2. The perimeter of a rectangle is 528 millimeters. The ratio of the length to the width is 8 : 3. Find the length and the width.
3. Solve 1 �
s � 8 �
3 � 36 .
4. Find the geometric mean of 42 and 12.
5. The extended ratio of the angles of a triangle is 5 : 12 : 13. Find the angle measures of the triangle.
6. The area of a rectangle is 720 square inches. If the ratio of the length to width is 5 : 4, fi nd the perimeter of the rectangle.
Warm-Ups: 1. 15 2. 15 3. 15 4. width: 25 m; length: 30 m
Lesson Quiz: 1. 2 : 3 2. 192 mm, 72 mm 3. 4 4. 6 ��
14 5. 30�, 72�, 78� 6. 108 in.
ANSWERS
Warm-Up ExercisesLESSON
6.2Co
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43Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH06.indd 43LAH_GE_11_FL_LT_CH06.indd 43 11/9/09 2:01:10 PM11/9/09 2:01:10 PM
1. Solve 12
� 10
� x � 60 .
2. The scale of a map is 1 cm : 10 mi. The actual distance between two towns is 4.3 miles. Find the length on the map.
3. A model train engine is 9 centimeters long. The actual engine is 18 meters long. What is the scale of the model?
Lesson QuizFor use after Lesson 6.2
1. In the diagram, RS
� XY
� ST
� YZ . Write four true proportions.
R T
S
4524
X Z
Y30
x
2. In the diagram, MR
� RN
� PS
� SN .
M
P
S
RN
20
12
18x
Find MN and MR.
3. On a map, a street is 2 inches long. The actual length is 1 mile. Find the scale.
4. A map is scaled so that 1 cm represents 20 km. If two towns are 8.2 centimeters apart on the map, what is the actual distance between the towns?
Warm-Ups: 1. 72 2. 0.43 cm 3. 1 cm : 2 m
Lesson Quiz: 1. Sample answer: 45
� 30
� 24
� x ; 30
� 45
� x � 24 ;
45 �
24 �
30 � x ;
45 � 30
� 30
� 24 � x
� x 2. 48; 30 3. 1 in. : 0.5 mi 4. 164 km
ANSWERS
Warm-Up ExercisesLESSON
6.3Co
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44Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH06.indd 44LAH_GE_11_FL_LT_CH06.indd 44 11/9/09 2:01:56 PM11/9/09 2:01:56 PM
1. In nABC and nXZW, m∠A � m∠X and m∠B � m∠Z. What can you conclude about m∠C and m∠W?
2. Solve x �
18 �
54 � 9 .
3. nABC � nDEF. Find x.
CA
B
8
12 FD
E
x
15
Lesson QuizFor use after Lesson 6.3
1. Determine whether the polygons
E G
H
F
30
26 22
16
K M
N
L 15
13 11
8 are similar. If they are, writea similarity statement and fi nd the scale factor of EFGH to KLMN.
2. In the diagram, nDEF � nHJK. Find the value of x.
D F
E
1012
H K
J
8
9x
3. Two similar triangles have the scale factor 5 : 4. Find the ratio of their corresponding altitudes and medians.
4. Two similar triangles have the scale factor 3 : 7. Find the ratio of their corresponding perimeters and areas.
Warm-Ups: 1. They are the same. 2. 108 3. 10
Lesson Quiz: 1. yes; EFGH � KLMN; the scale factor is 2 : 1. 2. 13.5 3. 5 : 4; 5 : 4 4. 3 : 7; 9 : 49
ANSWERS
Warm-Up ExercisesLESSON
6.4Co
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45Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH06.indd 45LAH_GE_11_FL_LT_CH06.indd 45 11/12/09 1:52:53 PM11/12/09 1:52:53 PM
Determine whether the two triangles are similar.
1. nABC: m∠A � 90�, m∠B � 44�; nDEF: m∠D � 90�, m∠E � 46�
2. nABC: m∠A � 132�, m∠B � 24�; nDEF: m∠D � 90�, m∠F � 24�
3. Solve 6 �
12 �
x � 1 � 8 .
Lesson QuizFor use after Lesson 6.4
Determine if the two triangles are similar. If they are, write a similarity statement.
1.
D C
BE
A
558
558
2. NM
Y
P
X
558 708
458 3. Find the length of � BC .
BA
D
8
E
12
5C
x
4. A tree casts a shadow that is 30 feet long. At the same time a per-son standing nearby, who is fi ve feet two inches tall, casts a shadow that is 50 inches long. How tall is the tree to the nearest foot?
Warm-Ups: 1. similar 2. not similar 3. 5
Lesson Quiz: 1. yes; nABE � nACD 2. no 3. 7.5 4. 37 ft
ANSWERS
Warm-Up ExercisesLESSON
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46Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH06.indd 46LAH_GE_11_FL_LT_CH06.indd 46 11/9/09 2:07:42 PM11/9/09 2:07:42 PM
1. Give the postulate or theorem that justifi es why the triangles are similar.
808
808
2. Solve 16
� 32
� 12 � x
� x .
Lesson QuizFor use after Lesson 6.5
1. Verify that nABC � nDEF for the given information. nABC: AC � 6, AB � 9, BC � 12; nDEF: DF � 2, DE � 3, EF � 4
2. Show that the triangles are similar and write a similarity statement. Explain your reasoning.
60
45
40
30
1508
1508
CA
ZX
B
Y
Warm-Ups: 1. AA Similarity Postulate 2. 8
Lesson Quiz: 1. AC
� DF � AB
� DE � BC
� EF � 3 � 1 . The ratios are
equal, so nABC � nDEF by the SSS Similarity Theorem.
2. XY
� AB
� YZ
� BC � 3 � 4 and ∠Y � ∠B. So nXYZ � nABC by the SAS
Similarity Theorem.
ANSWERS
Warm-Up ExercisesLESSON
6.6Co
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47Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH06.indd 47LAH_GE_11_FL_LT_CH06.indd 47 11/9/09 2:08:07 PM11/9/09 2:08:07 PM
Give the coordinates of a point twice as far from the origin along a ray from (0, 0).
1. (3, 5) 2. (�2, 0) 3. � 1 __ 2 , � 1 __ 2 � Give the coordinates of a point one-half as far from the origin along a ray from (0, 0).
4. (6, �4) 5. (0, �7)
Lesson QuizFor use after Lesson 6.6
Find the value of the variable.
1. 20
106
x
2.
x
12 16
18
3.
1410
y17
1 2
∠1 > ∠2
4. This diagram represents a tract
Webster Street
Center Street371.9 yd
80 yd
85 yd
120 yd 150 yd
Lot CLot A
Lot B40 yd
80 yd
110 yd
130 yd
of land being developed for homes. Which lot has the greatest perimeter?
Warm-Ups: 1. (6, 10) 2. (�4, 0) 3. (1, �1) 4. (3, �2) 5. (0, �3.5)
Lesson Quiz: 1. 12 2. 13.5 3. 23.8 4. Lot B
ANSWERS
Warm-Up ExercisesLESSON
6.7Co
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48Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH06.indd 48LAH_GE_11_FL_LT_CH06.indd 48 12/8/09 3:59:29 PM12/8/09 3:59:29 PM
1. Draw a dilation with scale factor 2 of nABC with vertices A(1, 0), B(0, 3), and C(3, 2). Label the image nDEF.
2. nABC has vertices A(0, 0), B(0, 8), and C(6, 0). Draw a dilation
of nABC using a scale factor of 1 �
2 . Label the image nDEF.
Lesson Quiz:
1.
F
E
C
A
B
D
1
x5
y 2.
FCA
B
D
E
1
x5
y
ANSWERS
Lesson QuizFor use after Lesson 6.7
LESSON
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GeometryWarm-Up Transparencies 49
LAH_GE_11_FL_LT_CH06.indd 49LAH_GE_11_FL_LT_CH06.indd 49 11/9/09 2:15:04 PM11/9/09 2:15:04 PM
1. Determine whether the polygons are similar. If they are, write a similarity statement and fi nd the scale factor of nABC to nDEF.
42 B
A
28
C
52.5
95°
D E12
8
F
15
2. In the fi gure below, if nJKL ~ nRST, fi nd the value of x.
18
x
12
6
159
J L
KS
R T
Lesson QuizFor use after 6.3 Focus On Patterns
1. Find the fi fth, sixth, seventh, and eighth terms of the Fibonacci sequence.
2. Find the ratios of the consecutive terms you found in Question 1.
Warm-Ups: 1. nABC ~ nDEF, 7 �
2 2. 10
Lesson Quiz: 1. 5, 8, 13, 21 2. 8 � 5 � 1.6,
13 �
8 � 1.625,
21 �
13 " 1.6154
ANSWERS
LESSON
6.3 Focus On PatternsWarm-Up Exercises
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GeometryWarm-Up Transparencies 50
LAH_GE_11_FL_LT_CH06.indd 50LAH_GE_11_FL_LT_CH06.indd 50 11/18/09 5:31:45 PM11/18/09 5:31:45 PM
1. Solve x2 5 100. 2. Solve x2 1 9 5 25.
3. Simplify Ï}
20 . 4. Find x.
x
10 cm10 cm
12 cm
Warm-Ups: 1. 10, 210 2. 4, 24 3. 2 Ï}
5 4. 6 cm
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Warm-Up ExercisesLESSON
7.1
51Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH07.indd 51LAH_GE_11_FL_LT_CH07.indd 51 11/9/09 3:01:03 PM11/9/09 3:01:03 PM
1. Find x.
5
x2
2. Simplify (5 Ï}
3 )2.
3. Find x. 12x
15
Lesson QuizFor use after Lesson 7.1
1. Find the length of the 2. Find the area of the hypotenuse of the right triangle. isosceles triangle.
36
x15
h 51 cm51 cm
48 cm
3. Find the unknown side length x.
126
x10Write your answer in simplest radical form.
Warm-Ups: 1. Ï}
29 2. 75 3. 9
Lesson Quiz: 1. 39 2. 1080 cm2 3. 4 Ï}
13
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Warm-Up ExercisesLESSON
7.2
52Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH07.indd 52LAH_GE_11_FL_LT_CH07.indd 52 11/9/09 3:01:38 PM11/9/09 3:01:38 PM
1. Are these triangles similar? If so, give the reason.
708
808
308
808
2. Find x. 14
x
48
Lesson QuizFor use after Lesson 7.2
1. Tell whether the triangle is a 51
4524
right triangle.
Decide if the segment lengths can form a triangle. If so, tell whether the triangle is acute, right, or obtuse.
2. 7, 11, 3 Ï}
17 3. 4.1, 9.2, 5.6
4. A playground has a slide, a swing, 50 ftSlide Swing
32 ft
Sandbox
48 ft
and a sandbox. The slide and the swing are 50 feet apart, the swing and sandbox are 32 feet apart, and the slide and sandbox are 48 feet apart. Do the three pieces of apparatus form a right triangle?
Warm-Ups: 1. Yes; the AA Similarity Postulate 2. 50
Lesson Quiz: 1. yes 2. yes; acute because 153 < 170 3. yes; obtuse because 84.64 > 48.17 4. no
ANSWERS
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Warm-Up ExercisesLESSON
7.3
53Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH07.indd 53LAH_GE_11_FL_LT_CH07.indd 53 11/13/09 7:01:31 PM11/13/09 7:01:31 PM
In Exercises 1–3, simplify.
1. 6 Ï}
2 p Ï}
2 2. 6 }
Ï}
3
3. 5 } Ï
}
2
4. Find m∠DBC in square ABCD.
D
A
C
B
Lesson QuizFor use after Lesson 7.3
1. Identify the three similar right triangles in the diagram.
X W Z
Y
Find the value of the variable.
2. 3.
a
6
4
x
5
9
Warm-Ups: 1. 12 2. 2 Ï}
3 3. 5 Ï
}
2 }
2 4. 458
Lesson Quiz: 1. nXYZ , nXWY , nYWZ 2. 3 Ï}
5 3. 2 Ï}
15
ANSWERS
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Warm-Up ExercisesLESSON
7.4
54Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH07.indd 54LAH_GE_11_FL_LT_CH07.indd 54 11/9/09 3:07:04 PM11/9/09 3:07:04 PM
Find the values of the variables.
1.
y
x6
4 2.
30 x
x
Lesson QuizFor use after Lesson 7.4
Use these triangles for Exercises 1–4.
a
ba
c
de
608
1. Find a if b 5 10 Ï}
2 . 2. Find b if a 5 19.
3. Find d and e if c 5 4. 4. Find c and d if e 5 50 Ï}
3 .
5. Find x, y, and z.
y
xz
458 308
6
Warm-Ups: 1. x 5 2 Ï}
6 , y 5 2 Ï}
15 2. 15 Ï}
2
Lesson Quiz: 1. 10 2. 19 Ï}
2 3. d 5 4 Ï}
3 , e 5 8
4. c 5 25 Ï}
3 , d 5 75 5. x 5 3 Ï}
2 , y 5 3 Ï}
6 , z 5 6 Ï}
2
ANSWERS
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Warm-Up ExercisesLESSON
7.5
55Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH07.indd 55LAH_GE_11_FL_LT_CH07.indd 55 11/9/09 3:08:29 PM11/9/09 3:08:29 PM
Use this diagram for Exercises 1–4.
Y
X Z
1. Name the hypotenuse. 2. Name the leg opposite ∠X.
3. Name the leg adjacent to ∠X. 4. If XY 5 17 and m∠X 5 418, fi nd YZ.
Lesson QuizFor use after Lesson 7.5
Use this diagram for Exercises 1–4.
C A
B
b
ca
1. If a 5 18, b 5 80, and c 5 82, fi nd tan B and tan A. Write each answer as a fraction and a decimal rounded to 4 places.
2. If a 5 17 and m∠A 5 318, fi nd b to the nearest tenth.
3. If a 5 9 and m∠B 5 748, fi nd b to the nearest tenth.
4. If a 5 5 and m∠B 5 798, fi nd the number of square units in the area of nABC to the nearest tenth.
Warm-Ups: 1. } XZ 2. } YZ 3. } XY 4. 14.78
Lesson Quiz: 1. tan B 5 40
} 9 5 4.4444;
tan A 5 9 } 40 5 0.2250 2. 28.3 3. 31.4 4. 64.3
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Warm-Up ExercisesLESSON
7.6
56Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH07.indd 56LAH_GE_11_FL_LT_CH07.indd 56 11/9/09 3:20:00 PM11/9/09 3:20:00 PM
Use this diagram for Exercises 1–4.
1. If PR 5 12 and m∠R 5 198, fi nd p.
2. If m∠P 5 588 and r 5 5, fi nd p.
P
R
r
p
q
3. If m∠P 5 608, and p 5 9, fi nd q.
4. If r 5 8 and p 5 12, fi nd q.
Lesson QuizFor use after Lesson 7.6
Use this diagram for Exercises 1–3.
1. If x 5 4 Ï}
5 , y 5 4, and z 5 4 Ï}
6 , fi nd sin X, sin Y, cos X, and cos Y.
Z
X
Y
y
x
z
2. If y 5 10 and m∠Y 5 158, fi nd z to the nearest tenth.
3. If z 5 12 and m∠X 5 848, fi nd y to the nearest tenth.
4. A lamppost is 11 feet tall. If the
498
11 ftx
angle of elevation through the top of the lamppost to the sun is 498, approximately how far is the top of the lamppost from the tip of its shadow?
Warm-Ups: 1. 11.3 2. 8.0 3. 10.4 4. 14.4
Lesson Quiz: 1. sin X 5 Ï
}
30 } 6 ø 0.9129, sin Y 5
Ï}
6 } 6 ø 0.4082,
cos X 5 Ï
}
6 } 6 ø 0.4082, cos Y 5
Ï}
30 } 6 ø 0.9129 2. 38.6
3. 1.3 4. 14.6 ft
ANSWERS
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Warm-Up ExercisesLESSON
7.7
57Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH07.indd 57LAH_GE_11_FL_LT_CH07.indd 57 11/9/09 3:23:02 PM11/9/09 3:23:02 PM
Use this diagram for Exercises 1–3.
Y Z
yz
x
X
1. If x 5 9 and z 5 11, fi nd m∠X to the nearest tenth of a degree.
2. If y 5 5 and z 5 12, fi nd m∠X to the nearest tenth of a degree.
3. If m∠Y 5 17.48 and z 5 12, solve nXYZ.
Lesson Quiz: 1. 54.98 2. 65.4° 3. The angles are 17.48, 72.68, and 908; the sides are 12, about 3.6, and about 11.5.
ANSWERS
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Lesson QuizFor use after Lesson 7.7
LESSON
7.7
GeometryWarm-Up Transparencies 58
LAH_GE_11_FL_LT_CH07.indd 58LAH_GE_11_FL_LT_CH07.indd 58 11/9/09 3:27:00 PM11/9/09 3:27:00 PM
1. Let nABC be a right triangle with acute /A. Defi ne sin A, cos A, and tan A.
AC
B
2. Find sin B, cos B, and tan B.
A C
B
25
15
20
Lesson QuizFor use after 7.6 Focus On Trigonometry
1. Find cot A, sec A, and csc A. Write each answer as a fraction and as a decimal to four places, if necessary.
C
A
B40
419
Warm-Ups: 1. sin A = BC
} AB
, cos A = AC
} AB
, tan A = BC
} AC
2. sin B = 3 } 5 , cos B =
4 } 5 , tan B =
3 }
4
Lesson Quiz: 1. cot A = 9 }
40 = 0.225, sec A =
41 }
9 ø 4.5556, csc A =
41 }
40 = 1.025
ANSWERS
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LESSON
7.6 Focus On TrigonometryWarm-Up Exercises
GeometryWarm-Up Transparencies 59
LAH_GE_11_FL_LT_CH07.indd 59LAH_GE_11_FL_LT_CH07.indd 59 11/12/09 12:56:24 PM11/12/09 12:56:24 PM
1. If the measures of two angles of a triangle are 19� and 80�, fi nd the measure of the third angle.
2. Solve (x � 2)180 � 1980.
3. Find the value of x.
548 x 8
Warm-Ups: 1. 81� 2. 13 3. 126
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH08.indd 60LAH_GE_11_FL_LT_CH08.indd 60 11/10/09 7:59:52 AM11/10/09 7:59:52 AM
1. Find the value of x.
988
1208
828x 8
2. Find the coordinates of the midpoint of � AB with endpoints A(�2, 6) and B(10, 4).
3. Find the distance between (�2, 6) and (10, 4).
Lesson QuizFor use after Lesson 8.1
1. Find the sum of the measures of the interior angles of a convex 24-gon.
2. The sum of the measures of the interior angles of a convex polygon is 5040�. Classify the polygon by the number of sides.
3. Find the value of x.
1108
468
728
x 8
(3x)8
4. Find the measure of an interior angle and an exterior angle of a regular 36-gon.
Warm-Ups: 1. 60 2. (4, 5) 3. 2 ��
37
Lesson Quiz: 1. 3960� 2. 30-gon 3. 33 4. 170�, 10�
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH08.indd 61LAH_GE_11_FL_LT_CH08.indd 61 11/10/09 9:02:47 AM11/10/09 9:02:47 AM
1. What congruence postulate shows that nABE � nCDE?
D C
A B
E
2. If ∠E � ∠G, fi nd m∠E.
G H
628
F E628
Lesson QuizFor use after Lesson 8.2
1. Find the values of a and b in the parallelogram.
36830
a 2 12(b 1 10)8
2. Find the measure of ∠K in the parallelogram.
648
J M
K L
Find the indicated measures in parallelogram ABCD.
3. m∠BCD
4. If BE � 9, fi nd BD. 378
1008
B CE
A D
Warm-Ups: 1. SAS 2. 118�
Lesson Quiz: 1. 42, 26 2. 116� 3. 43� 4. 18
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH08.indd 62LAH_GE_11_FL_LT_CH08.indd 62 11/12/09 1:49:04 PM11/12/09 1:49:04 PM
1. Give fi ve ways to prove that a quadrilateral is a parallelogram.
2. Find x in the parallelogram.
2x 1 105x 2 32
Lesson QuizFor use after Lesson 8.3
Tell how you know that the quadrilateral is a parallelogram.
1. 2.
808
808
1008
3. For what value of x is the 4. In a coordinate plane, draw the quadrilateral a parallelogram? quadrilateral ABCD with vertices
(x 1 30)8
2x 8 A(�1, 3), B(7, �1), C(6, �4), and D(�2, 0). Show that ABCD is a parallelogram.
Warm-Ups: 1. opp. sides �, opp. sides �, diags. bisects each other, opp. angles �, a pair of opp. sides � and � 2. 14
Lesson Quiz: 1. The diagonals bisect each other.2. Both pairs of opposite angles are congruent. You can also conclude that opposite sides are parallel and use the defi nition of a parallelogram. 3. 504. AB � CD � 4 �
� 5 and BC � AD � �
� 10 ,
so two pairs of opposite sides are congruent.
ANSWERS
1x
y
C
D
A
B22
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH08.indd 63LAH_GE_11_FL_LT_CH08.indd 63 11/10/09 9:12:51 AM11/10/09 9:12:51 AM
Use the fi gure to answer the questions.
A B
X Y
558 558
x 8 y 8
1. What are the values of x and y?
2. If �
› AX and
�
› BY intersect at point P, what kind of triangle is nXPY?
Lesson QuizFor use after Lesson 8.4
Name each type of quadrilateral (parallelogram, rectangle, rhombus, and square) for which the statement is true.
1. Both pairs of opposite angles are congruent.
2. The quadrilateral is equilateral.
3. Given rhombus MNOP, 4. Given rectangle QRST, fi nd m∠NPO. fi nd m∠RUS.
M P
N O488
T
U
R S
648
Warm-Ups: 1. 125, 125 2. isosceles
Lesson Quiz: 1. parallelogram, rectangle, rhombus, square 2. rhombus, square 3. 48� 4. 128�
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH08.indd 64LAH_GE_11_FL_LT_CH08.indd 64 11/12/09 1:48:49 PM11/12/09 1:48:49 PM
Find the value of x. 1. 1158
x 8
2.
x 8
308
3. x 8
208
Lesson QuizFor use after Lesson 8.5
1. Find m∠A, m∠C, and m∠D. 2. Find the length of the midsegment of the trapezoid.
17
33
A
C
D
B568
Use the fi gure to fi nd the indicated measures.
3. If m∠XYZ � 80� and m∠XWZ � 48�, fi nd m∠YZW.
X
YW
Z
O 4. If XO � 2, OZ � 2, YO � 6, and OW � 8, fi nd the lengths of the sides of the kite.
Warm-Ups: 1. 65 2. 120 3. 70
Lesson Quiz: 1. 124�, 56�, 124� 2. 25 3. 116�
4. 2 ��
10 , 2 ��
17
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH08.indd 65LAH_GE_11_FL_LT_CH08.indd 65 11/12/09 1:46:02 PM11/12/09 1:46:02 PM
1. Find the distance between the points A(1, �3) and B(�2, 4).
2. Determine if the triangles with the given vertices are similar.
A(�3, 3), B(�4, 1), C(�2, �1)
1
y
21 x
B
C
D
E
F
A D(3, 5), E(2, 1), F(4, �3)
Lesson QuizFor use after Lesson 8.6
For Exercises 1–3, write true or false.
1. The diagonals of a rectangle are always perpendicular.
2. The diagonals of a rhombus are always congruent.
3. One pair of opposite angles of a kite are congruent.
4. Give the most specifi c name for the quadrilateral. Explain.
5. Points A(1, 4), B(6, 21), C(1, 26), and D(24, 21) are the vertices of a quadrilateral. Give the most specifi c name for ABCD. Explain.
Warm-Ups: 1. ��
58 2. nABC and nDEF are not similar.
Lesson Quiz: 1. false 2. false 3. true 4. Rhombus; it is a � since two pairs of opp. � are �. Since two consec. sides are �, all sides are �. 5. Square; slope of } AB � slope of } CD � �1, slope of } BC � slope of } AD � 1. Opp. sides are �, so ABCD is a �. Two consec. sides are � and AB 5 BC 5 5 �
� 2 , so ABCD is a square.
ANSWERS
LESSON
8.7 Warm-Up ExercisesCo
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LAH_GE_11_FL_LT_CH08.indd 66LAH_GE_11_FL_LT_CH08.indd 66 11/18/09 7:23:55 PM11/18/09 7:23:55 PM
1. Find the side lengths of the quadrilaterals with the given vertices. Then determine if the quadrilaterals are congruent.
J(1, 1), K(2, 4), L(5, 4), M(4, 1); N(�1, �3), O(0, 0), P(4, 0), Q(3, �3)
2. Find the side lengths of the quadrilaterals with the given vertices. Then determine if the quadrilaterals are similar.
R(�2, 3), S(�2, 1), T(�4, 1), U(�4, 3); V(5, 2), W(5, �2), X(1, �2), Y(1, 2)
3. Without introducing any new variables, supply the missing coordinates for G so that EFGH is a rectangle.
y
x
G(?, ?)F(a, c)
E(a, b) H(d, b)
Lesson Quiz: 1. JK � LM � NO � PQ � ��
10 , KL � JM � 3 but OP � NQ � 4 ; not congruent 2. RS � ST � TU � RU � 2, VW � WX � XY � VY � 4; ratios of corresponding side lengths are equal; corresponding angles are congruent; similar 3. (d, c)
ANSWERS
Lesson QuizFor use after Lesson 8.7
LESSON
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LAH_GE_11_FL_LT_CH08.indd 67LAH_GE_11_FL_LT_CH08.indd 67 11/10/09 9:42:18 AM11/10/09 9:42:18 AM
1. What is a translation?
2. Translate A(3, 5) 4 units right and 2 units down. What are the coordinates of the image?
3. Find the length of } BC with endpoints B(23, 5) and C(1, 2).
4. If you translate the points M(4, 7) and N(21, 5) by using (x, y) → (x 2 3, y 1 6), what is the distance from M9 to N9?
Warm-Ups: 1. a transformation that moves every point of a fi gure the same distance in the same direction 2. (7, 3) 3. 5 4. Ï
}
29
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH09.indd 68LAH_GE_11_FL_LT_CH09.indd 68 11/12/09 1:41:47 PM11/12/09 1:41:47 PM
1. Write the component form of the
1
x
y
5
B9
A9
C9
B
AC
vector that translates nABC to nA9B9C9.
2. If P(28, 4) is translated by (x, y) → (x 1 6, y 1 1), what is the image of P?
Lesson QuizFor use after Lesson 9.1
1. The vertices of nXYZ are X(23, 2), Y(1, 1), and Z(21, 23). Graph the image of the triangle using prime notation after the translation (x, y) → (x 1 1, y 2 2).
2. Translate A(28, 6) using D
C
(x, y) → (x 2 7, y 1 10).
3. Name the vector and write it in component form.
4. Use the point M(8, 22). Find the component form of the vector that describes the translation to M9(7, 5).
Warm-Ups: 1. ⟨26, 21⟩ 2. (22, 5)
Lesson Quiz: 1.
1
x
y
24
YX
Z
Y9X9
Z9
2. (215, 16)
3. ### Y CD , ⟨4, 6⟩
4.⟨21, 7⟩
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH09.indd 69LAH_GE_11_FL_LT_CH09.indd 69 11/17/09 11:18:47 AM11/17/09 11:18:47 AM
1. The y-axis is the perpendicular bisector of } AB . If point A is at (23, 5), what is the location of point B?
2. What is the slope of the segment with endpoints at (27, 4) and (4, 27)?
3. Multiply F 21 0 0 1GF 6 22 1
3 4 7G.
Lesson QuizFor use after Lesson 9.2
Add or subtract
1. [2.8 29.2] 1 [3.5 6.1]
2. F 8 22 23 5 G 2 F 4 3
1 27G 3. Triangle ABC has vertices A(2, 21), B(1, 3), and C(22, 22).
Write a matrix equation that shows how to fi nd the image matrix that represents the translation of nABC 4 units left and 5 units up.
4. Multiply F 2 25 1 0GF 6 21
3 22G.
Warm-Ups: 1. (3, 5) 2. 21 3. F 26 2 21 3 4 7G
Lesson Quiz: 1. [6.3 23.1] 2. F 4 25 24 12G
3. F 24 24 24 5 5 5G 1 F 2 1 22
21 3 22 G 5 F 22 23 26 4 8 3G 4. F 23 8
6 21G
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH09.indd 70LAH_GE_11_FL_LT_CH09.indd 70 11/10/09 9:56:47 AM11/10/09 9:56:47 AM
1. Use a protractor to draw an angle with measure 208.
2. Given the points A(3, 5), B(25, 3), and the origin O(0, 0), fi nd OA, OB, and m∠BOA.
3. Multiply F 0 1 21 0GF 2 3
5 27G.
Lesson QuizFor use after Lesson 9.3
Graph the polygon and its refl ection in the given line.
1. Quadrilateral with vertices A(22, 1), B(1, 4), C(3, 1), D(2, 21) over y 5 1
2. Triangle P(22, 2), Q(3, 4), R(4, 1) over y 5 x
3. Use matrix multiplication to fi nd the image A B C
matrix when nABC is refl ected in the y-axis. F 2 21 0 3 4 21G
4. Find point C on the x-axis so AC 1 BC is a minimum for A(2, 5) and B(7, 3).
Warm-Ups: 1. 208
2. Ï}
34 , Ï}
34 , 908 3.
F 5 27 22 23G
Lesson Quiz: 1.
4
x
y
21
CC9
B
B9
AA9
D9
D
2.
1
x
y
21
9
R
R9
P
P9
3. A9 B9 C9 4. 1 41 }
8 , 0 2 F 22 1 0
3 4 21G
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH09.indd 71LAH_GE_11_FL_LT_CH09.indd 71 11/12/09 1:41:03 PM11/12/09 1:41:03 PM
Find the image of (2, 3) under each transformation.
1. translation (x, y) → (x 2 6, y 2 2)
2. refl ection in the y-axis
3. refl ection in the line y 5 6
4. rotation 908 about the origin
Lesson QuizFor use after Lesson 9.4
1. Construct an equilateral triangle DEF. Then draw the image of nDEF for a 308 rotation about the center C of the triangle.
In Exercises 2 and 3, use the quadrilateral HIJK with vertices H (3, 0), I(1, 24), J(0, 24), and K(21, 23).
2. Use the coordinate rules to name the vertices of the image of HIJK for a rotation of 1808 about the origin.
3. Use matrix multiplication to fi nd the image matrix that represents a 2708 rotation of HIJK about the origin. Then graph the polygon and its image.
Warm-Ups: 1. (24, 1) 2. (22, 3) 3. (2, 9) 4. (23, 2)
Lesson Quiz:
1. E
FD
E9
F 9
D 9
C
2. H9(23, 0), I9(21, 4), J9(0, 4), K9(1, 3)
3. H9 I9 J9 K9
F 0 24 24 23 23 21 0 1G
1
x
y
21
I
H
KJ
I9
J9
K9
H9
ANSWERS
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LAH_GE_11_FL_LT_CH09.indd 72LAH_GE_11_FL_LT_CH09.indd 72 11/12/09 1:40:44 PM11/12/09 1:40:44 PM
Find the coordinates of the image of A(23, 8) for each transformation.
1. Refl ection in the line y 5 x
2. Rotation of 908 about the origin
3. Translation 4 units down
Lesson QuizFor use after Lesson 9.5
1. The endpoints of } AB are A(3, 2) and B(1, 4). Graph the image of } AB after the glide refl ection. Translation: (x, y) → (x, y 2 2) Refl ection: in the line x 5 1
2. The vertices of nMNK are M(1, 1), N(2, 3), and K(0, 2). Graph the image of nMNK after the composition of the refl ection followed by the rotation. Refl ection: in the y-axis Rotation: 1808 about the origin
Warm-Ups: 1. (8, 23) 2. (28, 23) 3. (23, 4)
Lesson Quiz:
1.
2
x
y
21
B
AB 0B9
A9
x 5 1
A0
2.
1
x
y
21 M 0
N 0
K 0
N
M
K9N9
M9
K
ANSWERS
Warm-Up ExercisesLESSON
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73Geometry
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LAH_GE_11_FL_LT_CH09.indd 73LAH_GE_11_FL_LT_CH09.indd 73 11/12/09 1:40:20 PM11/12/09 1:40:20 PM
If nABC ~ nDEF, fi nd each value.
20
18
10
A
C
B
8D
F
E
1. EF 2. AC 3. scale factor
Lesson QuizFor use after Lesson 9.6
How many lines of symmetry does each fi gure have?
1. a rhombus that is not a square 2. equilateral triangle
Does the fi gure have rotational symmetry? If so, describe the rotations that map the fi gure onto itself.
3. 4.
Warm-Ups: 1. 36
} 5 2. 25 3. 5 }
2
Lesson Quiz: 1. 2 2. 3 3. yes; 728, 1448 4. no
ANSWERS
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LAH_GE_11_FL_LT_CH09.indd 74LAH_GE_11_FL_LT_CH09.indd 74 11/10/09 10:00:57 AM11/10/09 10:00:57 AM
1. Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Find the value of x.
3 2
2x
C
P 9
P
2. Find the image matrix that represents a dilation of nXYZ with vertices X(3, 2), Y(8, 21), and Z(21, 21) centered at the origin
with scale factor 1 }
2 . Then graph the polygon and its image.
Lesson Quiz: 1. 5 }
3 ; enlargement; 1.2
2. X' Y' Z'
F 1.5 4 20.5
1 20.5 20.5 G
ANSWERS
1
x
y
6
Y
X
Y 9
ZZ9
X 9
LESSON
9.7 Lesson QuizFor use after Lesson 9.7
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LAH_GE_11_FL_LT_CH09.indd 75LAH_GE_11_FL_LT_CH09.indd 75 11/10/09 10:01:20 AM11/10/09 10:01:20 AM
What is the measure of each interior angle of each regular polygon?
1. equilateral triangle
2. pentagon
3. hexagon
4. octagon
5. Draw a trapezoid and its image for a refl ection in one base.
Lesson QuizFor use after 9.5 Focus On Patterns
1. Make a tessellation using a rectangle. Change both pairs of opposite sides.
2. Describe the transformation(s) used to make the tessellation.
Warm-Ups: 1. 60° 2. 108° 3. 120° 4. 135° 5.
Lesson Quiz:
1. Sample: 2. translation and refl ection, or translation and rotation
ANSWERS
LESSON
9.5 Focus On PatternsWarm-Up Exercises
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LAH_GE_11_FL_LT_CH09.indd 76LAH_GE_11_FL_LT_CH09.indd 76 11/13/09 7:14:17 PM11/13/09 7:14:17 PM
1. What measure is needed to fi nd the circumference or area of a circle?
2. Find the radius of a circle with diameter 8 centimeters.
3. A right triangle has legs with lengths 5 inches and 12 inches. Find the length of the hypotenuse.
4. Solve 6x 1 15 5 33.
5. Solve (x 1 18)2 5 x2 1 242.
Warm-Ups: 1. radius or diameter 2. 4 cm 3. 13 in. 4. 3 5. 7
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH10.indd 77LAH_GE_11_FL_LT_CH10.indd 77 11/10/09 10:51:08 AM11/10/09 10:51:08 AM
Find x and y.
1. x 8
y 8
1208 2.
x 8y 8
408
708
Lesson QuizFor use after Lesson 10.1
1. Give the name that best 2. Tell how many common describes the fi gure. tangents the circles have.
B
E
C
P FD
A
a. ‹ ]
› CD b.
‹ ] › AB c. } FD d. } EP
3. Is } AB tangent to (C? Explain. 4. Find x.
B C
A
34
30 16
A
D
B
2x 1 11
3x 2 1
C
Warm-Ups: 1. x 5 60; y 5 60 2. x 5 35; y 5 35
Lesson Quiz: 1. a. secant, b. tangent, c. chord, d. radius 2. One tangent; it is a vertical line through the point of tangency. 3. Yes; 162 1 302 5 1156 5 342 so } AB ⊥ } AC , and a line ⊥ to a radius at its endpoint is tangent to the circle. 4. 12
ANSWERS
Warm-Up ExercisesLESSON
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78Geometry
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LAH_GE_11_FL_LT_CH10.indd 78LAH_GE_11_FL_LT_CH10.indd 78 11/12/09 1:34:34 PM11/12/09 1:34:34 PM
Tell whether the segment is best described as a radius, chord, or diameter of (C.
BA
DE
C
1. } DC 5. Solve 4x 5 8x 2 12.
2. } BD 6. Solve 3x 1 2 5 6x 2 4.
3. } DE
4. } AE
Lesson QuizFor use after Lesson 10.2
Use this diagram of (F for Exercises 1–4.
Describe each arc as a minor arc, major arc,
CE
AB
F328
or semicircle. Find the arc measure.
1. C BC
2. C CBE
3. C BCE
4. Explain why C AE > C BC .
5. Two diameters of (P are } AB and } CD . If m C AD 5 508, fi nd m C ACD and m C AC .
Warm-Ups: 1. radius 2. diameter 3. chord 4. chord 5. 3 6. 2
Lesson Quiz: 1. minor arc, 328 2. major arc, 2128 3. semi-circle, 1808 4. m∠AFE 5 m∠BFC because the angles are
vertical angles, so ∠AFE > ∠BFC. Then arcs C AE and C BC are arcs that
have the same measure in the same circle. By defi nition C AE > C BC . 5. 3108; 1308
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH10.indd 79LAH_GE_11_FL_LT_CH10.indd 79 11/12/09 1:34:16 PM11/12/09 1:34:16 PM
1. The measure of the interior angles of a quadrilateral are 808, 1008, 558, and 5x8. Find the value of x.
2. Two supplementary angles have measures 6x8 and 12x8. Find each angle measure.
3. Solve 3x 5 1 } 2 (4x 1 12). 4. Solve 80 5
1 } 2 (360 2 2x).
Lesson QuizFor use after Lesson 10.3
Find the value of x in (C. Explain.
1.
C
3x 5x 2 12
2.
18C
4x 1 2
3. Determine whether } RS R
S
T UV
is a diameter. Explain.
Warm-Ups: 1. 25 2. 608; 1208 3. 6 4. 100
Lesson Quiz: 1. 6; If a diameter of a circle is ⊥ to a chord, then the diameter bisects the chord and its arc. 2. 4; In the same circle, if two chords are equidistant from the center, then they are >. 3. Yes. Sample answer: } RS is the ⊥ bisector of } TU by Theorem 5.3. Then } RS is a diameter of the circle by Theorem 10.4.
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH10.indd 80LAH_GE_11_FL_LT_CH10.indd 80 11/12/09 1:32:36 PM11/12/09 1:32:36 PM
Solve for x.
1. 2x 5 84 1 32 2. x 5 1 } 2 (360 2 120)
3. 180 2 x 5 1 } 2 ((2x 1 4) 1 28)
4. One-half of the measure of an angle plus the angle’s supplement is equal to the measure of the angle. Find the measure of the angle.
Lesson QuizFor use after Lesson 10.4
Find the value of x.
1.
768
x 8
2.
288
x 8 3.
448
x 8
Find the value of each variable.
4. 1008
4y 8728
2x 8
5.
15x 89.5y 8
8.5y 821x 8
Warm-Ups: 1. 58 2. 120 3. 82 4. 1208
Lesson Quiz: 1. 38 2. 56 3. 44 4. x 5 54; y 5 20 5. x 5 5; y 5 10
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH10.indd 81LAH_GE_11_FL_LT_CH10.indd 81 11/10/09 10:53:41 AM11/10/09 10:53:41 AM
Solve the equation.
1. x2 1 4x 1 3 5 0 2. 6x 2 9 5 x2
3. 3(x 1 4) 5 (2 1 4)(4) 4. 21(x 2 4) 5 (2x 2 7)(x 1 2)
5. If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number.
Lesson QuizFor use after Lesson 10.5
Line t is tangent to the circle. Find the value of x and y. 1.
t
2308
x 8
2.
688
368
x 8
3.
228 728
y 8
4.
t278
1358x 8
y 8
Warm-Ups: 1. 21, 23 2. 3 3. 4 4. 5, 7 5. 47.6
Lesson Quiz: 1. 115 2. 52 3. 25 4. x 5 81, y 5 40.5
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH10.indd 82LAH_GE_11_FL_LT_CH10.indd 82 11/10/09 10:54:17 AM11/10/09 10:54:17 AM
Evaluate each expression.
1. Ï}}
(10 2 2)2 1 (8 1 7)2
2. Ï}}
(23 2 2)2 1 (28 2 4)2
3. In a map on a coordinate grid, two towns are at coordinates (2, 3) and (21, 4). If each unit on the grid is 1 kilometer, whatis the distance between the towns?
Lesson QuizFor use after Lesson 10.6
Find the value of x. Round to the nearest hundredth, if necessary.
1.
10
4
20
x
2.
18 4
x
x 1 1
3.
16
9
x
4.
45
40
18
x
5.
8 16x
x
Warm-Ups: 1. 17 2. 13 3. Ï}
10 km or about 3.16 km
Lesson Quiz: 1. 2 2. 8 3. 15 4. 20.25 5. 11.31
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH10.indd 83LAH_GE_11_FL_LT_CH10.indd 83 11/10/09 10:55:44 AM11/10/09 10:55:44 AM
1. Write the standard equation of a circle with center (23, 5) and radius 2.
2. Graph the circle (x 1 1)2 1 ( y 2 3)2 5 9.
3. The line x 5 2 is tangent to the circle in Exercise 2. Find the coordinates of the point of tangency.
4. A circle has equation x2 1 y2 5 4. Determine whether line y 5 2x 1 2 is a secant, tangent, or neither.
Lesson Quiz: 1. (x 1 3)2 1 ( y 2 5)2 5 4
2.
1
x
y
21
3. (2, 3) 4. secant
ANSWERS
LESSON
10.7 Lesson QuizFor use after Lesson 10.7
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84Geometry
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LAH_GE_11_FL_LT_CH10.indd 84LAH_GE_11_FL_LT_CH10.indd 84 11/10/09 10:56:28 AM11/10/09 10:56:28 AM
1. List the properties that make a quadrilateral a parallelogram.
2. Solve x2 1 x2 5 102.
3. Solve 28 5 1 } 2 x(8).
4. Solve 12x 5 84.
Warm-Ups: 1. Opposite sides are congruent and parallel; opposite angles are congruent; consecutive angles are supplementary;
diagonals bisect each other 2. Ï}
51 3. 7 4. 7
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH11.indd 85LAH_GE_11_FL_LT_CH11.indd 85 11/10/09 10:57:28 AM11/10/09 10:57:28 AM
1. Find the area of a parallelogram with height 12 feet and base 8 feet.
2. Find the area of an isosceles triangle with sides 20, 20, and 24 units.
3. What is the length of the midsegment of a trapezoid with bases 10 inches and 15 inches?
4. Solve 200 5 1 } 2 x(18 1 22).
Lesson QuizFor use after Lesson 11.1
Find the area of the polygon.
1.
20
24
2.
24
40
3. ABCE 4.
33 ft
19 ft20 ft
25 30
15
18
A
F
B
D E
C
5. Find the area of a triangle with side lengths 13 inches, 13 inches, and 10 inches.
Warm-Ups: 1. 96 ft2 2. 192 square units 3. 12.5 in. 4. 10
Lesson Quiz: 1. 480 square units 2. 480 square units 3. 375.4 square units 4. 973.5 ft2 5. 60 in.2
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH11.indd 86LAH_GE_11_FL_LT_CH11.indd 86 11/12/09 11:20:05 AM11/12/09 11:20:05 AM
1. Two polygons are similar and the ratio of corresponding sides is 3 : 4. What is the ratio of the perimeters?
2. Solve 12
} x 5
18 } 6 .
3. A rectangle has area 108 square feet and the length is three times the width. What are the dimensions of the rectangle?
Lesson QuizFor use after Lesson 11.2
Find the area of each fi gure.
1. BA
CD1
x
y
21
2. 8 cm
36 cm
3.
13 ft
13 ft
15 ft
5 ft
4. 20 ft
38 ft
16 ft
5. The height of a trapezoid is 8 feet. One base is twice as long as the other, and the area is 72 square feet. How long is each base?
Warm-Ups: 1. 3 : 4 2. 4 3. 18 ft by 6 ft
Lesson Quiz: 1. 20 square units 2. 144 cm2 3. 135 ft2 4. 1072 ft2
5. 6 ft; 12 ft
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH11.indd 87LAH_GE_11_FL_LT_CH11.indd 87 11/10/09 11:11:12 AM11/10/09 11:11:12 AM
Simplify the expression.
1. 45
} 360
2. 120
} 360
(9π) 3. 15π
} 3 4.
60 }
360 (15π)
5. A central angle of a circle measures 828. Find the measure of the intercepted arc.
6. Solve 3.8
} x 5
120 } 360 .
Lesson QuizFor use after Lesson 11.3
Figure I~Figure II. Find the ratio of the perimeters and the ratio of the areas. Then fi nd the unknown area.
1.
24 ft
18 ftI
II
A 5 60 ft2
2.
18 cm
12 cmI
II
A 5 780 cm2
3. Rectangle I ~ Rectangle II. In Rectangle I, the length is 20 feet and the perimeter is 64 feet. In Rectangle II, the width is 8 yards. Find the ratio of the area of Rectangle I to the area of Rectangle II.
Warm-Ups: 1. 1 }
8 2. 3π 3. 5π 4.
5π }
2 5. 828 6. 11.4
Lesson Quiz:
1. ratio of perimeters: 4 : 3; ratio of areas: 16 : 9; 33.75 ft2
2. ratio of perimeters: 2 : 3; ratio of areas: 4 : 9; 346 2 }
3 cm2 3. 1: 4
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH11.indd 88LAH_GE_11_FL_LT_CH11.indd 88 11/10/09 11:14:08 AM11/10/09 11:14:08 AM
Find the area of a circle with the given measure.
1. Radius: 8 cm 2. Radius: 1 1 }
3 mi 3. Circumference: 4π ft
4. Solve x2 5 100
} π .
Lesson QuizFor use after Lesson 11.4
Find the indicated measure.
1. Circumference 2. Radius 3. length of C AB
13 in.
r
C 5 48 ft
9 cm
A
B558
4. Find the total circumference 32 cm
16 cm
of the circles.
Find the indicated measure.
5. Radius 6. Circumference
P r
42 cm
1108
92.8 in.
1508
Warm-Ups: 1. about 201.06 cm2 2. about 5.59 mi2 3. 4π ft2 4. about 65.64
Lesson Quiz: 1. about 81.68 in. 2. about 7.64 ft 3. 8.64 cm 4. 100.53 cm 5. about 21.88 cm 6. about 222.72 in.
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH11.indd 89LAH_GE_11_FL_LT_CH11.indd 89 11/10/09 11:33:29 AM11/10/09 11:33:29 AM
1. An isosceles triangle has side lengths 20 meters, 26 meters, and 26 meters. Find the length of the altitude to the base.
2. Solve 18 5 1 } 2 p x.
3. Evaluate (4 cos 108)(10 sin 208).
4. Evaluate 10 }
tan 888 .
Lesson QuizFor use after Lesson 11.5
1. Find the area of the 2. Use the area of the sector to fi nd sectors formed by ∠DEF. the area of (R.
9 in.
D
EF
1508
R
1108
A 5 64.5 cm2
3. Find the area of the shaded region.
6 ft
18 ft
Warm-Ups: 1. 24 m 2. 36 3. 13.47 4. 0.3492
Lesson Quiz: 1. 106.03 in.2, 148.44 in.2 2. 211.09 cm2 3. 23.18 ft2
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH11.indd 90LAH_GE_11_FL_LT_CH11.indd 90 11/12/09 1:27:20 PM11/12/09 1:27:20 PM
1. Find the area of a circle with radius 5.2 cm.
2. Find the area of a right triangle with hypotenuse 18 in. and side length 8 in.
3. A rectangle with sides 4 inches and 5 inches is cut out of a square with sides 8 inches. Find the area that remains.
Lesson QuizFor use after Lesson 11.6
1. Find the measure of a central angle of a regular polygon with 24 sides.
Find the area of each regular polygon.
2.
5.5 cm
8.0 cm 3.
12 cm6 3 cm
Find the perimeter and area of each regular polygon.
4.
15 in.
5.
4 m
Warm-Ups: 1. 84.9 cm2 2. 64.5 in.2 3. 44 in.2
Lesson Quiz: 1. 158 2. 110 cm2 3. 374.1 cm2 4. 99.4 in.; 745.6 in.2 5. 22.6 m; 32 m2
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH11.indd 91LAH_GE_11_FL_LT_CH11.indd 91 11/10/09 11:37:32 AM11/10/09 11:37:32 AM
1. Find the probability that a point chosen at random on } JN is on } KN .
0 42
L M NJ K
222426
2. Find the probability that a randomly chosen point
4
in the fi gure will lie in the shaded region.
3. A bird is equally likely to be anywherein the garden shown. What is the
flowers
vegetables
probability that the bird will be in the vegetables?
Lesson Quiz: 1. 5 } 7 or 71.4% 2. 36.3% 3. about
24 }
51 or 47%
ANSWERS
LESSON
11.7 Lesson QuizFor use after Lesson 11.7
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LAH_GE_11_FL_LT_CH11.indd 92LAH_GE_11_FL_LT_CH11.indd 92 11/10/09 11:41:49 AM11/10/09 11:41:49 AM
1. Find the length of a 60° arc in a circle with radius 8 meters.
2. Find the exact value of x if 12 }
2p • 8 5
x }
360 .
Find the exact length of the arc.
3. C ACB 4. C AB
P
C
20 m
A
B
P
A
B
608
Circumference 5 80 cm
Lesson QuizFor use after 11.4 Focus On Reasoning
Use the diagram and the given arc measure to fi nd thedistance between points A and B. Leave your answers in terms of p.
1. m C AB 5 80º 2. m C AB 5 100º
A P
B
C9
A P
B
C18
Warm-Ups: 1. about 8.38 m 2. 270
} p 3. 30p m 4. 13 1 } 3 cm
Lesson Quiz: 1. 2p 2. 5p
ANSWERS
LESSON
11.4 Focus On ReasoningWarm-Up Exercises
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LAH_GE_11_FL_LT_CH11.indd 93LAH_GE_11_FL_LT_CH11.indd 93 11/25/09 2:36:58 PM11/25/09 2:36:58 PM
Name the polygon by the number of sides.
1. 6 2. 10 3. 5
4. What is a regular polygon?
5. What is the length of the diagonal of a square with side length 6?
Warm-Ups: 1. hexagon 2. decagon 3. pentagon 4. a polygon with all congruent sides and all congruent angles 5. 6 Ï
}
2
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH12.indd 94LAH_GE_11_FL_LT_CH12.indd 94 11/11/09 11:59:28 AM11/11/09 11:59:28 AM
1. Evaluate 2xy 1 2yz 1 2xz for x 5 9, y 5 6, and z 5 4.
2. Evaluate 2πx2 1 2πxy for x 5 4 and y 5 7. Use 3.14 for π.
3. Find the area of a circle with radius 8 cm. Use 3.14 for π.
4. Find the area of a right triangle with hypotenuse 13 in. and a side length of 5 in.
5. Find the area of a regular pentagon with apothem 4.13 ft and side length 6 ft.
Lesson QuizFor use after Lesson 12.1
Determine whether the solid is a polyhedron. If it is, name it. 1. 2. 3.
4. Find the number of faces, vertices, and edges of each polyhedron in Exercises 2 and 3.
5. A plane intersects a cone, but does not intersect the base of the cone. Describe the possible cross sections.
Warm-Ups: 1. 228 2. 276.32 3. 200.96 cm2 4. 30 in.2 5. 61.95 ft2
Lesson Quiz: 1. no 2. yes; rectangular pyramid 3. yes; pentagonal prism 4. pyramid: 5 faces, 5 vertices, 8 edges; prism: 7 faces, 10 vertices, 15 edges 5. a point, a circle, an ellipse
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH12.indd 95LAH_GE_11_FL_LT_CH12.indd 95 11/11/09 12:01:17 PM11/11/09 12:01:17 PM
Find the area of each regular polygon or circle.
1. Hexagon, radius 8 cm 2. Circle, radius 4 in.
3. Inscribed pentagon, radius 1 yd
4. Find the perimeter of an inscribed square with radius 1 ft.
5. Find the circumference of a circle with diameter 12.8 in.
Lesson QuizFor use after Lesson 12.2
1. Find the surface area of the
16 cm
4 cm solid formed by the net.
Find the surface area and lateral area of the right prism or right cylinder.
2.
25 m
15 m 38 m
3.
26 yd
20 yd
4. A rectangular prism has surface
8 ft
30 ft
x ft
area 1848 ft2. Solve for x.
Warm-Ups: 1. 166.28 cm2 2. 50.27 in.2 3. 2.38 yd2 4. 5.66 ft 5. 40.21 in.
Lesson Quiz: 1. 288 cm2 2. 2580 m2, 2280 m2 3. 2261.95 yd2, 1633.63 yd2 4. 18
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH12.indd 96LAH_GE_11_FL_LT_CH12.indd 96 11/10/09 1:44:31 PM11/10/09 1:44:31 PM
Find the area of each polygon or circle.
1. Trapezoid, bases 12 ft and 18 ft, height 3 ft
2. Circle, diameter 8.2 in.
3. Regular hexagon, side length 14 cm
Lesson QuizFor use after Lesson 12.3
1. Find the lateral area of the 2. Find the surface area of the cone. regular pyramid. Round to the nearest hundredth.
10 cm
15 cm
12 in.
36 in.
3. A right cone has radius 8 m and surface area 224π m2. Find its slant height.
Warm-Ups: 1. 45 ft2 2. 52.8 in.2 3. 509.22 cm2
Lesson Quiz: 1. 300 cm2 2. 1882.97 in.2 3. 20 m
ANSWERS
Warm-Up ExercisesLESSON
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LAH_GE_11_FL_LT_CH12.indd 97LAH_GE_11_FL_LT_CH12.indd 97 11/10/09 2:01:46 PM11/10/09 2:01:46 PM
Find the area of each polygon or circle.
1. Regular hexagon, side length 9 in.
2. Circle, radius 15 m
3. Right triangle, hypotenuse 12 cm, side length 6 cm
4. Solve (2 Ï
}
3 )2 Ï}
3 }
12 p x 5 15 Ï
}
3 .
Lesson QuizFor use after Lesson 12.4
1. Find the volume of the solid with regular pentagonal bases.
14.5 in.
15 in.
10 in. 2. Find the volume of a right triangular prism
with height 32 in., base height 12 in., and base length 18 in.
3. Find the volume of a right cylinder with height 30 ft and diameter 14 ft.
4. A cylindrical beaker with diameter 10 in. and height 12 in. is fi lled with water that is then poured into a rectangular pan that is 14 in. by 9 in. by 3 in. What is the volume of each solid? Would the water overfl ow the pan? If so, what is the height of the water in the beaker after the pan is fi lled?
Warm-Ups: 1. 210.44 in.2 2. 706.86 m2 3. 31.18 cm2 4. 15
Lesson Quiz: 1. 5437.5 in.3 2. 3456 in.3 3. 4618.14 ft3 4. cylinder: 942.48 in.3; pan: 378 in.3; Yes, it would overfl ow the pan. After the pan is fi lled, the height of the water in the beaker will be about 7.2 in.
ANSWERS
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LAH_GE_11_FL_LT_CH12.indd 98LAH_GE_11_FL_LT_CH12.indd 98 11/10/09 2:39:37 PM11/10/09 2:39:37 PM
Find the area of each circle.
1. Radius 17 m 2. Diameter 7.8 in.
Find the volume of each solid.
3. Cylinder, radius 6 ft, height 10 ft
4. Cone, radius 3.1 cm and height 11.8 cm
5. Find the circumference of a circle with radius 48 m.
Lesson QuizFor use after Lesson 12.5
Find the volume of each solid.
1.
8 in.
6 in.
2.
12 mm
24 mm
3. Find the volume of the cube afterthe cone is removed.
6.8 mm
6.8 mm
6.8 mm 4. The volume of a right cone with
height 32 in. and radius r in. is 2144.66 in.3. Find r.
Warm-Ups: 1. 907.92 m2 2. 47.78 in.2 3. 1130.97 ft3 4. 118.75 cm3 5. 301.59 m
Lesson Quiz: 1. 96 in.3 2. 3619.11 mm3 3. 232.11 mm3 4. 8.0 in.
ANSWERS
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LAH_GE_11_FL_LT_CH12.indd 99LAH_GE_11_FL_LT_CH12.indd 99 11/10/09 2:40:07 PM11/10/09 2:40:07 PM
Find the surface area and volume of each solid.
1. Right rectangular prism, side lengths 8 in., 5 in., and 10 in.
2. Right cone, radius 3 m, height 4 m
3. Sphere, radius 7.3 ft
Lesson QuizFor use after Lesson 12.6
Find the surface area and volume of each sphere.
1.
r 5 6 ft
2.
d 5 12.4 m
3. A great circle of a sphere has circumference 16π in. Find the volume of the sphere.
4. Find the radius of a sphere with volume 4445.18 ft3.
5. Find the surface area and volume of the solid. 4 m
4 m
Warm-Ups: 1. 340 in.2; 400 in.3 2. 75.40 m2; 37.70 m3 3. 669.66 ft2; 1629.51 ft3
Lesson Quiz: 1. 452.39 ft2; 904.78 ft3 2. 483.05 m2; 998.31 m3 3. 2144.66 in.3 4. 10.2 ft 5. 251.33 m2; 335.10 m3
ANSWERS
Warm-Up ExercisesLESSON
12.7Co
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100Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH12.indd 100LAH_GE_11_FL_LT_CH12.indd 100 11/10/09 2:40:53 PM11/10/09 2:40:53 PM
1. Two triangular prisms are similar, with surface areas 9 ft2 and 25 ft2. What is the scale factor of the prisms?
2. Two spheres have volume 125π m3 and 216π m3. What is the scale factor of the spheres? What is the ratio of the surface areas?
3. The volumes of two similar square pyramids are 8 ft3 and 27 ft3. What is the ratio of the surface area of the smaller pyramid to the larger?
4. The two solids are similar. Find the surface area and volume of Solid II.
III
2.5 cm
5 cm
6 cm
Lesson Quiz: 1. 3 : 5 2. 5 : 6; 25 : 36 3. 4 : 9 4. S 5 361.28 cm2; V 5 575.96 cm3
ANSWERS
Lesson QuizFor use after Lesson 12.7
LESSON
12.7Co
pyrig
ht ©
Hol
t McD
ouga
l. Al
l rig
hts
rese
rved
.
101Geometry
Warm-Up Transparencies
LAH_GE_11_FL_LT_CH12.indd 101LAH_GE_11_FL_LT_CH12.indd 101 11/10/09 2:41:26 PM11/10/09 2:41:26 PM