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M A N E U V E R I N G T H E M I D D L E .C O M
PA G E T W O
ANGLES & TRIANGLES UNITTable of Contents
©Maneuvering the Middle LLC, 2016
PAGE TOPIC RESOURCE4 Sample Pacing Guide
5-6 Ideas for Implementation & Helpful Hints
7-16 Binder Covers, Dividers, and Spine Labels
17-18 Complementary and Supplementary Angles Student Handout 1
19 Complementary and Supplementary Angles Homework 1
21-22 Vertical and Adjacent Angles Student Handout 2
23 Vertical and Adjacent Angles Homework 2
25 Angle Relationships Mini-Quiz Mini-Quiz 1
27-28 Classifying Triangles Student Handout 3
29 Classifying Triangles Homework 3
31-32 Constructing Triangles Student Handout 4
33 Constructing Triangles Homework 4
35-36 Triangle Conditions Student Handout 5
37 Triangle Conditions Homework 5
39 Triangles Mini-Quiz Mini-Quiz 2
41-48 Angles and Triangles Unit Study Guide Study Guide
49-52 Angles and Triangles Unit Test Test
DAY 1 DAY 2 DAY 3 DAY 4 DAY 5
Complementary & Supplementary Angles
Vertical & Adjacent Angles
Classifying Triangles Constructing Triangles Triangle Conditions
Student Handout 1Homework 1
Student Handout 2Homework 2Mini-Quiz 1
Student Handout 3Homework 3
Student Handout 4Homework 4
Student Handout 5Homework 5
DAY 6 DAY 7 NOTES
Angles & Triangles Unit Study Guide
Angles & Triangles Unit Test
Unit Study Guide Unit Test
©Maneuvering the Middle LLC, 2017
ANGLES AND TRIANGLES PACING GUIDE
*NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy.
Ideas for Implementation: This bundle has all of the notes, homework, quizzes, and tests to make your life easier and to help your students to be successful with angle relationships and triangle concepts. A sample pacing guide is included for those of you who do not have a district scope and sequence or if it is very general. Additionally, an answer key is included.
If you notice any discrepancies in the documents or have any questions, please email me at: [email protected].
STANDARDS
7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle
7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
ANGLES AND TRIANGLESStudent Handouts
©Maneuvering the Middle LLC, 2016
HELPFUL HINTS
A few ideas for organizing your curriculum and keeping things nice and neat:
Keep each unit in a separate binder and use the spine labels and covers to keep them looking nice and easy to find. I personally love 1.5” binders.
©Maneuvering the Middle LLC, 2016
Student Handouts
BINDERS
I place my originals in page protectors in chronological order. Any extra copies from that lesson, I hole punch and place behind that page. When I need an extra or a student is missing something from weeeeeeeeks ago, I can simply pull out a copy.
PAGE PROTECTORS
I highlight the edges of my answer keys or if I am really good, print them on colored paper. It helps them to stand out and makes them easy to find on my desk, in a binder, by the document camera, etc. Plus, highlighter doesn’t show up if you make a copy.
ANSWER KEYS
Card stock in a page protector makes an awesome divider. When I set up my dividers, I include one for handouts, activities, assessments, and answer keys. Binder covers and spine labels have been included. J
CARD STOCK
Happy Teaching!
ANGLES ANDTRIANGLES
©MANEUVERINGTHEMIDDLE,2016
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ANGLES AND TRIANGLES
s e v e n t h G r a d e C u r r i c u l u m
U n i t s i x : A N S W E R K E Y S
©MANEUVERINGTHEMIDDLE,2016
ANGLES AND TRIANGLES
s e v e n t h G r a d e C u r r i c u l u m
U n i t s i x : A C T I V I T I E S
©MANEUVERINGTHEMIDDLE,2016
ANGLES AND TRIANGLES
s e v e n t h G r a d e C u r r i c u l u m
U n i t s i x : A S S E S S M E N T S
TYPE OF ANGLE DEFINITION EXAMPLE
ACUTEANGLE
An angle that measures ______________________ 90°
OBTUSEANGLE
An angle that measures _________________ 90° and _______
RIGHTANGLE
An angle that measures ______________________ 90°
STRAIGHTANGLE
An angle that measures ______________________ 180°
COMPLEMENTARYANGLES
A pair of angles that have a ____________of ____________
SUPPLEMENTARYANGLES
A pair of angles that have a ____________of ____________
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesStudent Handout 1
COMPLEMENTARY AND SUPPLEMENTARY ANGLES
©Maneuvering the Middle LLC, 2016
Angles can be ______________ many ways based on their ___________________ .
The protractor shows the measure of many different angles. Use the diagram to answer the questions below.
A
B
C
D
E
F• What is the measure of ∠CFE? __________
• What is the measure of ∠AFC? __________
1.
Equation: ___________________________
2.
Equation: ___________________________
Practice finding missing angles below. Be sure to justify your answers using specific vocabulary.
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
Draw a picture to represent the situation below. Then, write an equation and solve.
5. Two angles are complementary. One of the angles measures 15o. What is the measure of the second angle?
6. ∠ABE and ∠DBE are supplementary angles. If the measure of ∠ABE is 61o, then what is the measure of ∠DBE?
Use what you know about complementary and supplementary angles to write an equation to find the missing angle measure, x.
x
74ox136o
WRITINGEQUATIONS
• By writing and solving equations, we can determine the missing angle
______________________in various angle relationships.
3. The m∠1 = 42.8o.
a. Write an equation: ______________________
b. Find the measure of ∠2. ________________
c. How do you know?
4. The m∠2 = 65.6o.
a. Write an equation: ______________________
b. Find the measure of ∠1. ________________
c. How do you know?
∠1
∠2 ∠2∠1
1. m∠AFC 2. m∠CFB 3. m∠AFD 4. m∠EFC
5. Name three sets of supplementary angles.
______________ and ______________
______________ and ______________
______________ and ______________
6. Name two sets of complementary angles.
______________ and ______________
______________ and ______________
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesHomework 1
©Maneuvering the Middle LLC, 2016
Use the protractor to measure each angle and answer the questions below.
7. Complete the table below. Not every box will have an answer.
ANGLE MEASURE ANGLECLASSIFICATION
ITS COMPLEMENTARY ANGLE
ITS SUPPLEMENTARYANGLE
32°
75°
90°
68°
161°
136°
COMPLEMENTARY AND SUPPLEMENTARY ANGLES
A
B
C
D
E
F
ANGLE PAIR DEFINITION EXAMPLES RELATIONSHIP
VERTICALANGLES
Pairs of _________________ angles
formed by __________________ lines
∠____ and ∠____
∠____ and ∠____
ADJACENT ANGLES
Two angles that share a common
____________ and a common ____________
∠____ and ∠____
∠____ and ∠____
In the picture below, Lines X and Y are straight lines that intersect. Use a protractor to measure each of the 4 angles that were formed and complete the table.
• What do you notice about the angle measures?
• What do you notice about the sum of all four angles above?
1.
x = ________
angle pair __________________
2.
x = ________
angle pair __________________
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesStudent Handout 2
©Maneuvering the Middle LLC, 2016
Angles are ______________ when two lines ___________________.
∠A ∠B
∠C∠D
Two types of special angles are formed when two lines intersect. Use the picture above and the table to help you define and describe these types of angle pairs.
35ox
148o
x
VERTICAL AND ADJACENT ANGLES
Line X
Line Y
Use what you know about intersecting lines to label the missing angles in the pictures below.
m∠A: __________
m∠B: __________
m∠C: __________
m∠D: __________
6.
a. Equation: ________________
b. m ∠K ___________
c. Equation: ________________
d. m ∠M ___________
7.
a. Equation: ________________
b. m ∠G ___________
c. Equation: ________________
d. m ∠J ___________
8.
a. Equation: ________________
b. m ∠Z ___________
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
Angle relationship allow us to determine any unknown _____________________ .
All angles around a ____________________________ will always have a sum of ________.
40o
60o
32o 29o
112o
∠P ∠M
∠K
∠G
∠J ∠Z
Use your understanding of angle relationships to set up and solve an equation to find the missing angle measures.
3.
Equation: _________________
Value of x: ___________
Angle Measures: ___________
4.
Equation: _________________
Value of x: ___________
Angle Measures: ___________
5.
Equation: _________________
Value of x: ___________
Angle Measures: ___________
x
117o
94o
Set up and solve equations to find the missing angle measurements in each of the following.
x
141o
2x3x
20
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesHomework 2
_______________ ________________________________________
WHAT DIY TOOLS DO YOU USE IN MATH?
W: 76o Y: 25o T: 44o N: 90o U: 20o
L : 23o H: 119o M: 106o P: 148o C: 95o
A: 107o E: 17.3o D: 67o R: 45o I: 48o
3 6 1 9 8 2 1 5 4 7 ©Maneuvering the Middle LLC, 2016
Answer each question below. Match your answers in the table to solve the riddle.
VERTICAL AND ADJACENT ANGLES
1. Find the value of x. 2. Find the value of x. 3. Find the value of x.
4. If the measure of ∠ADC is 50°, then what is the measure of ∠BDC?
5. Find the value of x. 6. Find the value of x.
7. Find the measure of ∠1. 8. If the measure of ∠AED is 89°, then what is the measure of ∠CED?
9. Find the value of x.
94o x
117o148o
x
68ox
174o
32.7o
x
A
B
CD
125o
x
30o120o
6x
∠1
105o
30o
29o
x
12o
162o
(3x + 30)o
A B
C
DE
S
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesMini-Quiz 1
ANGLE RELATIONSHIPS MINI-QUIZ
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1. Angle 1 and Angle _______ are supplementary angles.
2. Angle 4 and Angle _______ are vertical angles.
3. Angles 3 and Angle _______ are adjacent angles.
4. Find the value of x.
x = __________
5. Find the missing angle measure.
__________
6. Angles 1 and 2 are complementary. If ∠1 measures 29.6°, then what is the measure of ∠2?
__________
Use your understanding of angle relationships to solve the questions below.
134o x
30ox
89o
44o
∠1 ∠2
∠3 ∠4
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesMini-Quiz 1
ANGLE RELATIONSHIPS MINI-QUIZ
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1. Angle 1 and Angle _______ are supplementary angles.
2. Angle 4 and Angle _______ are vertical angles.
3. Angles 3 and Angle _______ are adjacent angles.
4. Find the value of x.
x = __________
5. Find the missing angle measure.
__________
6. Angles 1 and 2 are complementary. If ∠1 measures 29.6°, then what is the measure of ∠2?
__________
Use your understanding of angle relationships to solve the questions below.
134o x
30ox
89o
44o
∠1 ∠2
∠3 ∠4
©Maneuvering the Middle LLC, 2016
ANGLES OF A TRIANGLE
• Triangles are named by the three angles. Angles can be named in two
different ways:
Ex: Triangle ABC is shown at right.
• ∠A can also be called angle ______or ______.
• ∠ B can also be called angle ______or ______.
• ∠ C can also be called angle ______or ______.
• The _________ of the three angles in a triangle is _________.
• Using information about the triangle, you can set up an
___________________ to determine any missing angle measures.
SIDE LENGTHS OF A TRIANGLE
• The side length of a triangle corresponds with the angle measure
___________________ the side.
Ex: Triangle ABC is shown at right.
• Side AB corresponds with angle ______.
• Side BC corresponds with angle ______.
• Side CA corresponds with angle ______.
• The smallest angle will be opposite the ___________________ side, while
the largest angle will be opposite the ___________________ side.
• A side is ___________________ to another side if it has an equal length.
A
B
C
A
C
B
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesStudent Handout 3
CLASSIFYING TRIANGLES
SIDE
LEN
GTH EQUILATERAL ISOSCELES SCALENE
ANGLE
M
EASU
RE
ACUTE RIGHT OBTUSE
Triangles can be _________________ according to their side length and angle measure.
©Maneuvering the Middle LLC, 2016
T
62o
V
W
X
28.7o
N
M O
41.4o
77.2o
R
P
Q
US
1. Use each of the images above to answer the questions about angle measure and side length.
a. Which side corresponds to angle MNO? ________b. Which side corresponds to angle TUS? ________c. Which side corresponds to angle VXW? ________d. Which angle will be the smallest in triangle PQR? ________e. Which angle will be the largest in triangle MNO? ________f. How can angle MON be classified? ________________
56o
2. Find the measure of ∠ B. 3. Find the measure of ∠ F. 4. Find the measure of ∠ HIG.
5. Triangle JHL has angle HLJ, which measures 65o, and angle LJH, which measures 50o. Draw a sketch of triangle JHL and determine the missing angle measure.
Determine the missing angle in the triangles below.
45o32o 81oA
B E
DC
F
G
H
I58o
51o
6. 7. 8.
Classify the triangles below based on side length and angle measure. Find the missing angle.
ΔGHI
side: ___________________
angle: __________________
x = _________
ΔABC ΔDEF
side: ___________________
angle: __________________
x = ________
side: ___________________
angle: __________________
x = _________
xoA
B
C
xo
118o34o
D E
F xo
57o
G
H
I
Summarize today’s lesson:
1. Determine which sides correspond with each angle in triangle ABC below.
2. In triangle QRS, the measure of angle RSQ is 29.1o, and the measure of angle QRS is 80o. What is the measure of angle SQR?
A. 109.1°B. 71.1°C. 150.9°D. 70.9°
3. Triangle DEF is shown below. What is the measure of ∠D?
4. Triangle NOP is shown below. What is the measure of ∠N?
A. 47.3o
B. 137.3o
C. 48.8o
D. 132.8o
5. In triangle EFG, the measure of angle E is 97o, and the measure of angle F is 15o. What is the measure of angle G?
6. Determine which angles correspond with each side in the triangle below.
7. Determine if the measurements below will create a triangle. Then, explain your thinking.
Name _____________________________________Date _____________________________Pd ______
Unit: Angles & TrianglesHomework 3
Answer each of the questions below. Be sure to show your thinking.
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Y
X
Za. angle XYZ corresponds with side length ______
b. angle ZXY corresponds with side length ______
c. angle YZX corresponds with side length ______
D
F
E
42.7o
N
P O
a. side length KL corresponds with angle ______
b. side length LJ corresponds with angle ______
c. side length JK corresponds with angle ______
K
LJ
ANGLE MEASURES TRIANGLE? HOW DO YOU KNOW?
a. 70o, 90o, 20o
b. 55o, 45o, 75o
c. 27o, 27o, 126o
CLASSIFYING TRIANGLES
TRIANGLE INEQUALITY
THEOREM
• In order for a triangle to be formed, the sum of any ___________ sides
must be ___________________ the length of the third side.
Ex: Triangle ABC has side lengths of A = 7cm and B = 9cm.
1. the greatest C could be is ___________
2. the shortest C could be is ___________
3. ___________
• When three lengths meet the triangle inequality theorem, then
______________________ triangle will be formed.
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesStudent Handout 4
CONSTRUCTING TRIANGLES
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In order to construct a triangle, you will need to be familiar with using a ruler and protractor to measure.
3. Using your protractor practice constructing the angles below.
75o angle 105o angle 29o angle
1. Three line segments have measures of 13 units, 7 units, and 5 units. Will the segments form a triangle?
1- ___________________
2- ___________________
3- ___________________
Does it form a triangle?
2. Three line segments have measures of 4 units, 6 units, and 8 units. Will the segments form a triangle?
1- ___________________
2- ___________________
3- ___________________
Does it form a triangle?
Use the triangle inequality theorem to answer the questions below.
ANGLE SUM
• The _________ of the three angles in a triangle is _________.
• We can determine if the conditions lend themselves to creating one
triangle, more than one triangle, or will not create a triangle.
Use the steps above to construct a triangle with the given constraints.
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
4. A triangle with angle measures of 45o, 45o, and 90o
5. A triangle with angle measures of 65o, 40o, and 75o
6. A triangle ABC, where the m∠A = 30o, the m∠B = 80o, and the length of AB is 6 cm
7. A triangle ABC, where the m∠A = 40o, the m∠B = 60o, and the length of AB is 6 cm
TRIANGLE CONSTRUCTIONS
Triangle constructions are similar to constructing angles but require
more _____________ . Use the steps below to construct a triangle.
1. Start with a beginning point.
2. Use a protractor to draw the _____________________ angle.
3. Measure the line segment, if necessary.
4. Draw the second angle at the ______________________ .
5. Check all angle measures and side lengths.
1. Follow the steps below to construct a triangle.
a. sketch RS = 7cmb. draw angle R so that it is measures 35o
c. draw angle S so that it measures 55o
2. Use a ruler and protractor to construct ΔABC with AB = 3 cm, ∠ABC = 40o, and ∠BAC = 70o.
3. Use a ruler and protractor to construct ΔABC with m∠A = 40o, m∠B = 65o, and m∠C = 75o.
4. Three line segments have measures of 18 units, 12 units, and 10 units. Will the segments form a triangle?
1- ___________________
2- ___________________
3- ___________________
Does it form a triangle?
5. Three line segments have measures of 11 units, 6 units, and 3 units. Will the segments form a triangle?
1- ___________________
2- ___________________
3- ___________________
Does it form a triangle?
Name _____________________________________Date _____________________________Pd ______
Unit: Angles & TrianglesHomework 4
Answer each of the questions below. Be sure to show your thinking.
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CONSTRUCTING TRIANGLES
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesStudent Handout 5
TRIANGLE CONDITIONS
©Maneuvering the Middle LLC, 2016
GIVEN CONDITIONS DOES IT FORM A TRIANGLE? SKETCH AN EXAMPLE
THREE SIDES
When three sides are given, if the side
lengths meet the
____________________________, then they
will form a _____________ triangle.
TWO SIDES AND AN ANGLE
When two sides and an included angle are
given, then they will form a _____________
triangle.
TWO ANGLES AND ONE SIDE
When two angles and one side are given,
if the angles have a sum of
____________________________, then they
will form a _____________ triangle.
THREE ANGLES
When three angles are given, if the
angles meet the
____________________________, then they
will form _____________________ triangle.
Use the given information about each triangle below to predict whether the triangle is unique or not.
A
C
B
K
LJF
D
E58o
54o
G
H
I
68o
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
Use your understanding of the triangle inequality theorem to complete the table.
SIDE LENGTH HOW MANY TRIANGLES ARE FORMED? HOW DO YOU KNOW?
1. 7 cm, 8 cm, 9 cm
2. 1.5 cm, 3 cm, 1.5 cm
3. 4 in, 2 in, 8 in
4. 5 m, 5 m, 5 m
Use your understanding of the angle sum theorem to complete the table.
ANGLE MEASUREs HOW MANY TRIANGLES ARE FORMED? HOW DO YOU KNOW?
5. 70o, 90o, 20o
6. 55o, 45o, 75o
7. 27o, 27o, 126o
8. 39o, 87o, 55o
Apply your understanding of triangle constraints to answer the questions below.
9. Two sides of a triangle have lengths of 7 and 15. Which inequalities represent the possible lengths for the third side, x?
A. 8 < x < 22
B. 8 < x < 15
C. 7 < x < 15
D. 8 < x < 7
10. Which three angle measures cannot be the angle measures of a triangle?
A. 110o, 43o, 27o
B. 89o, 47o, 32o
C. 95o, 32o, 53o
D. 100o, 30o, 50o
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesHomework 5
©Maneuvering the Middle LLC, 2016
Apply your understanding of triangle conditions to answer the questions below.
1. Which three lengths could be the lengths of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm
B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm
D. 21 cm, 7 cm, 6 cm
2. Which three lengths cannot be the lengths of the sides of a triangle?
A. 23 m, 17 m, 14 m
B. 11 m, 11 m, 12 m
C. 5 m, 7 m, 8 m
D. 21 m, 6 m, 10 m
3. Which of the following will NOT produce a triangle?
A. angle measures of 47o, 58o, 75o
B. angle measures of 61o, 61o, 58o
C. side lengths of 5.5 ft, 11 ft, and 5.5 ft
D. side lengths of 5 in, 7 in, and 8 in
4. Two sides of a triangle have lengths of 5 and 9. Which inequalities represent the possible lengths for the third side, x?
A. 4 < x < 15
B. 14 < x < 19
C. 5 < x < 9
D. 4 < x < 14
TRIANGLE CONDITIONS
5. Use the given conditions below to mark the appropriate columns.
GIVEN CONDITIONS NO TRIANGLEUNIQUE
TRIANGLEMORE THAN ONE
TRIANGLE
a. a triangle with two 40o angles that surround a 5 inch side
b. a triangle with side lengths of 6 meters, 9 meters, and 8 meters
c. a triangle with angle measures of 63o, 44o, and 83o
d. a triangle with a 6 centimeter side, an 8-centimeter side, and an included angle of 40o
e. a triangle with angle measures of 60o, 90o, and 30o
1. What is the missing angle measure?
x = _________
2. Classify the triangle below by side and by measure.
side = ______________
measure = ______________
3. In triangle QRS, the measure of angle RSQ is 29.1o, and the measure of angle QRS is 76o. What is the measure of angle SQR?
__________
4. Three line segments have measures of 13 units, 7 units, and 5 units. Will the segments form a triangle?
__________
5. Determine if ΔABC with m∠A = 40o, m∠B = 65o, and m∠C = 75o will form more than one triangle or a unique triangle.
___________________
xo
57o
G
H IA
B
C
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesMini-Quiz 2
TRIANGLES MINI-QUIZ
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Use your understanding of triangle relationships to solve the questions below.
1. What is the missing angle measure?
x = _________
2. Classify the triangle below by side and by measure.
side = ______________
measure = ______________
3. In triangle QRS, the measure of angle RSQ is 29.1o, and the measure of angle QRS is 76o. What is the measure of angle SQR?
__________
4. Three line segments have measures of 13 units, 7 units, and 5 units. Will the segments form a triangle?
__________
5. Determine if ΔABC with m∠A = 40o, m∠B = 65o, and m∠C = 75o will form more than one triangle or a unique triangle.
___________________
xo
57o
G
H IA
B
C
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesMini-Quiz 2
TRIANGLES MINI-QUIZ
©M
aneuveri
ng t
he M
iddle
LLC
, 2016
Use your understanding of triangle relationships to solve the questions below.
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesReview - CCSS
Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.
I CAN CLASSIFY ANGLE RELATIONSHIPS. 7.G.5
1. The relationship between
∠2 and ∠3…2. The relationship
between∠2 and ∠3…3. The relationship between
∠3 and ∠4…
4. The relationship between
∠1 and ∠3…5. The relationship between
∠1 and ∠3…6. The relationship between
∠2 and ∠3…
©Maneuvering the Middle LLC, 2016
ANGLES AND TRIANGLES UNIT STUDY GUIDE
I CAN USE COMPLEMENTARY & SUPPLEMENTARY ANGLES TO WRITE & SOLVE EQUATIONS. 7.G.5
7.
Equation: __________________
x : ________
∠ measures: _____________
8.
Equation: __________________
x : ________
∠ measures: _____________
9. Two angles are supplementary. The first angle is 4x degrees. The second angle is (2x+6) degrees. Determine the measure of each angle.
Equation: __________________
x : ________
∠ measures: _____________
2x + 24xx
x-18
∠1
∠1
∠2 ∠3
∠4∠5
∠2
∠3
∠1 ∠4
∠2 ∠3 ∠1
∠4
∠5
∠2
∠3
∠1
∠4 ∠2
∠3 ∠1
∠2
∠3
I CAN USE VERTICAL AND ADJACENT ANGLES TO WRITE AND SOLVE EQUATIONS. 7.G.5
10.
Equation: __________________
x : ________
∠ measures: _____________
11.
Equation: __________________
x : ________
∠ measures: _____________
12.
Equation: __________________
x : ________
∠ measures: _____________
©Maneuvering the Middle LLC, 2016
37o
x
54o
x + 352x
3x - 6
78o2x
I CAN APPLY KNOWLEDGE OF TRIANGLES. 7.G.5
13. Use the triangle at right to answer the questions.
a. angle XYZ corresponds with side length ______
b. angle ZXY corresponds with side length ______
c. angle YZX corresponds with side length ______
14. Find the missing angle measure in each triangle below.
15. Which three lengths could be the lengths of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm D. 21 cm, 7 cm, 6 cm
A CB88o
33o
L
M
N29.4o
79o
Q
R
S 40o 40o
X
Y
Z
X
Y
Z
I CAN CONSTRUCT TRIANGLES. 7.G.5
20. Use the line segment below to construct atriangle with a ruler and a protractor.
• one obtuse angle• one side measures 4 cm
21. Use the line segment below to construct a triangle with a ruler and a protractor.
• one 45o angle• all sides have different measures in length
©Maneuvering the Middle LLC, 2016
I CAN CLASSIFY TRIANGLES.
16. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
17. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
18. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
19. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
A
C
G
HI
xo32o
F
E58o
xo
4.8 in
4.5 in
D68o
J
K
6 cm
xoL
6 cm
I’VE GOT IT!What concepts can I ace on the test?
HELP!What concepts do I need to study?
©Maneuvering the Middle LLC, 2016
I CAN DETERMINE THE CONDITIONS FOR A UNIQUE TRIANGLE, MORE THAN ONE TRIANGLE, OR NO TRIANGLE. 7.G.5
The cards below contain clues. Determine whether the conditions will result in one unique triangle, more than one triangle, or no triangle. Justify your solution with a sketch and description below.
22. Card A: ____________________________________________________________________________
_______________________________________________________________________________________
23. Card B: ____________________________________________________________________________
_______________________________________________________________________________________
24. Card C: ___________________________________________________________________________
_______________________________________________________________________________________
25. Two sides of a triangle have lengths of 9 and 18. Which inequality represents the possible length for the third side, x?
A. 9 < x < 18
B. 18 < x < 9
C. 9 < x < 27
D. 18 < x < 27
26. Which three lengths could be the lengths of the sides of a triangle?
A. 4 cm, 8 cm, 13 cm
B. 13 cm, 11 cm, 24 cm
C. 5 cm, 18 cm, 12 cm
D. 25 cm, 8 cm, 16 cm
ΔABC
AB IS 6.3 CM
BC IS 4.2 CMCA IS 10.4 CM
ΔABC
AB IS 2 CM
BC IS 3 CMCA IS 5 CM
ΔABC
∠A IS 80O
∠B IS 42O
∠C IS 58O
A B C
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesReview
Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.
I CAN CLASSIFY ANGLE RELATIONSHIPS.
1. The relationship between
∠2 and ∠3…2. The relationship
between∠2 and ∠3…3. The relationship between
∠3 and ∠4…
4. The relationship between
∠1 and ∠3…5. The relationship between
∠1 and ∠3…6. The relationship between
∠2 and ∠3…
©Maneuvering the Middle LLC, 2016
ANGLES AND TRIANGLES UNIT STUDY GUIDE
I CAN USE COMPLEMENTARY & SUPPLEMENTARY ANGLES TO WRITE & SOLVE EQUATIONS.
7.
Equation: __________________
x : ________
∠ measures: _____________
8.
Equation: __________________
x : ________
∠ measures: _____________
9. Two angles are supplementary. The first angle is 4x degrees. The second angle is (2x+6) degrees. Determine the measure of each angle.
Equation: __________________
x : ________
∠ measures: _____________
2x + 24xx
x-18
∠1
∠1
∠2 ∠3
∠4∠5
∠2
∠3
∠1 ∠4
∠2 ∠3 ∠1
∠4
∠5
∠2
∠3
∠1
∠4 ∠2
∠3 ∠1
∠2
∠3
I CAN USE VERTICAL AND ADJACENT ANGLES TO WRITE AND SOLVE EQUATIONS.
10.
Equation: __________________
x : ________
∠ measures: _____________
11.
Equation: __________________
x : ________
∠ measures: _____________
12.
Equation: __________________
x : ________
∠ measures: _____________
©Maneuvering the Middle LLC, 2016
37o
x
54o
x + 352x
3x - 6
78o2x
I CAN APPLY KNOWLEDGE OF TRIANGLES.
13. Use the triangle at right to answer the questions.
a. angle XYZ corresponds with side length ______
b. angle ZXY corresponds with side length ______
c. angle YZX corresponds with side length ______
14. Find the missing angle measure in each triangle below.
15. Which three lengths could be the lengths of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm D. 21 cm, 7 cm, 6 cm
A CB88o
33o
L
M
N29.4o
79o
Q
R
S 40o 40o
X
Y
Z
X
Y
Z
I CAN CONSTRUCT TRIANGLES.
20. Use the line segment below to construct atriangle with a ruler and a protractor.
• one obtuse angle• one side measures 4 cm
21. Use the line segment below to construct a triangle with a ruler and a protractor.
• one 45o angle• all sides have different measures in length
©Maneuvering the Middle LLC, 2016
I CAN CLASSIFY TRIANGLES.
16. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
17. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
18. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
19. Determine the missing value, x. Then, classify the triangle by side and by angle measure.
x: __________
by side: __________________________
by angle measure: _________________________
A
C
G
HI
xo32o
F
E58o
xo
4.8 in
4.5 in
D68o
J
K
6 cm
xoL
6 cm
I’VE GOT IT!What concepts can I ace on the test?
HELP!What concepts do I need to study?
©Maneuvering the Middle LLC, 2016
I CAN DETERMINE THE CONDITIONS FOR A UNIQUE TRIANGLE, MORE THAN ONE TRIANGLE, OR NO TRIANGLE. 7.G.5
The cards below contain clues. Determine whether the conditions will result in one unique triangle, more than one triangle, or no triangle. Justify your solution with a sketch and description below.
22. Card A: ____________________________________________________________________________
_______________________________________________________________________________________
23. Card B: ____________________________________________________________________________
_______________________________________________________________________________________
24. Card C: ___________________________________________________________________________
_______________________________________________________________________________________
25. Two sides of a triangle have lengths of 9 and 18. Which inequality represents the possible length for the third side, x?
A. 9 < x < 18
B. 18 < x < 9
C. 9 < x < 27
D. 18 < x < 27
26. Which three lengths could be the lengths of the sides of a triangle?
A. 4 cm, 8 cm, 13 cm
B. 13 cm, 11 cm, 24 cm
C. 5 cm, 18 cm, 12 cm
D. 25 cm, 8 cm, 16 cm
ΔABC
AB IS 6.3 CM
BC IS 4.2 CMCA IS 10.4 CM
ΔABC
AB IS 2 CM
BC IS 3 CMCA IS 5 CM
ΔABC
∠A IS 80O
∠B IS 42O
∠C IS 58O
A B C
Name _____________________________________Date ______________________________Pd______
Unit: Angles & TrianglesTest
Solve the problems below. Be sure to show your thinking.
©Maneuvering the Middle LLC, 2016
1. Which of the angles below are vertical angles?
A. ∠1 and ∠3 B. ∠3 and ∠4
C. ∠4 and ∠3 D. ∠4 and ∠1
2. Determine which equation below can be solved to find the value of ∠A.
A. x + 45 + 63 = 180
B. x + 90 + 63 = 180
C. x + 45 + 63 = 90
D. x + 90 + 63 = 360
3. Using the diagram below, determine whichstatement is NOT true.
A. angle Y is 90o
B. angles X and Z are complementary
C. angles X and Z are supplementary
D. angles Y and Z are adjacent
4. Daniel is given the following information to construct a triangle. Determine what type of triangle will be constructed.
80o, 40o, and 40o angles
A. a unique triangle
B. more than one triangle
C. no triangle
D. a right triangle
5. What is the measure of ∠J?
___________
6. Which three lengths cannot be the lengths
of the sides of a triangle?
A. 23 m, 17 m, 14 m
B. 11 m, 11 m, 12 m
C. 5 m, 7 m, 8 m
D. 21 m, 6 m, 10 m
ANGLES AND TRIANGLES UNIT TEST
J
K
6 cm
L6 cm
45o
63o
∠1∠2
∠3∠4
∠A
∠X
∠Y
∠B
∠Z
©Maneuvering the Middle LLC, 2016
Use the protractor below to answer questions 7-10.
7. What is the measure of ∠BFC?
A. 60o
B. 110o
C. 70o
D. 140o
8. Which of the following is a set of complementary angles?
A. ∠CFD and ∠EFD
B. ∠AFB and ∠DFE
C. ∠AFC and ∠DFC
D. ∠BFC and ∠DFE
9. Which pair of angles is an example of supplementary angles?
A. ∠AFB and ∠EFC
B. ∠AFC and ∠DFE
C. ∠AFD and ∠DFC
D. ∠AFD and ∠EFD
10. Which of the following is NOT a true statement?
A. ∠EFC measures 80o
B. ∠BFC and ∠DFE have a sum of 90o
C. ∠AFD measures 30o
D. ∠AFB and ∠CFD are complementary
11. Using the triangle below, set up and solve an equation in order to find the value of x.
___________
12. Find the measure of the largest angle in the diagram below.
___________
A
B
C
D
E
F
3x + 10
2x
xo
118o34.6oQ R
S
©M
aneuveri
ng t
he M
iddle
LLC
, 2016
13. Various pieces of string are cut at different lengths. Stephanie selects three pieces that measure 4.5 cm, 6 cm, and 8.5 cm. Determine what type of triangle Stephanie will form.
A. a unique triangle
B. more than one triangle
C. no triangle
D. a right triangle
14. Two sides of a triangle have lengths of 7 ftand 15 ft. Which inequality represents the possible length for the third side, x?
A. 8 < x < 22
B. 8 < x < 15
C. 7 < x < 15
D. 8 < x < 7
15. Which of the following is a true statementabout the triangle below?
A. It is an isosceles triangle.
B. It is an acute triangle.
C. It has one obtuse angle.
D. It has two equal side lengths.
16. The measure of ∠1 is 95o. Which of the following is NOT a true statement about the angles shown below?
A. The measure of ∠3 is 95o.
B. The measure of ∠4 is 105o.
C. The measure of ∠2 is 85o.
D. ∠2 and ∠ 4 are vertical angles.
17. What is unique about an equilateral triangle?
A. All sides are congruent.
B. All angles are obtuse.
C. The measures of two angles are congruent.
D. None of the sides are congruent.
18. In triangle JKL, ∠ J measures 25o, and ∠ K is a right angle. What is the measure of ∠ L?
___________
19. Using the diagram below, determine whichstatement is correct.
A. The measure of ∠ABC is 77o.
B. The measure of ∠BCA is obtuse.
C. The measure of ∠CAB is 23o.
D. The value of x is 29.
20. Which of the following classifications best represents the triangle below?
A. scalene
B. obtuse
C. acute
D. isosceles
44o
77o
N
L
M
∠1∠2
∠3∠4
(2x-5)o
62oA
B
Cxo
45o