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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




DAY 6 DAY 7 NOTES

Angles & Triangles Unit Study Guide

Angles & Triangles Unit Test

Unit Study Guide Unit Test


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


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.


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


U n i t s i x : A N S W E R K E Y S




U n i t s i x : A C T I V I T I E S




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


STRAIGHTANGLE


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


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.


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


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______



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 ___________



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: ___________


5.

Equation: _________________

Value of x: ___________


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______


_______________ ________________________________________

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.


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______


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.


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


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______


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.


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


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 ______


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______


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?


1- ___________________

2- ___________________

3- ___________________


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.



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.


1- ___________________

2- ___________________

3- ___________________



1- ___________________

2- ___________________

3- ___________________


Name _____________________________________Date _____________________________Pd ______


Answer each of the questions below. Be sure to show your thinking.

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CONSTRUCTING TRIANGLES

Name _____________________________________Date ______________________________Pd______


TRIANGLE CONDITIONS


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



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______



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 = ______________


__________


__________

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______


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 = ______________


__________


__________

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______


TRIANGLES MINI-QUIZ

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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…


∠1 and ∠3…5. The relationship between


∠2 and ∠3…


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: _____________


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 ______



14. Find the missing angle measure in each triangle below.


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


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: _________________________


x: __________

by side: __________________________

by angle measure: _________________________


x: __________

by side: __________________________

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?


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


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.


∠2 and ∠3…2. The relationship

between∠2 and ∠3…3. The relationship between

∠3 and ∠4…




∠2 and ∠3…


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: _____________


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 ______



14. Find the missing angle measure in each triangle below.


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


I CAN CLASSIFY TRIANGLES.


x: __________

by side: __________________________

by angle measure: _________________________


x: __________

by side: __________________________

by angle measure: _________________________


x: __________

by side: __________________________

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?


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


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.


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


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

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