000200010271960393 Unit1 Inv1-3 p001-023.qxd 11/21/15 4:25 ...gms7math.weebly.com/uploads/9/2/6/0/9260091/cmp3... · 17 Investigation 3 Copyright © Pearson Education, Inc., or its

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1. Which of these angles are acute, which are obtuse, and which are right?

a. b. c.

d. e. f.

Name ____________________________________________ Date ____________ Class ____________

Additional PracticeShapes and Designs

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2. Use the diagram of the polygon shown below to answer the following questions.

a. Estimate the measures of each angle.

Angle A: Angle B:

Angle C Angle D:

Angle E:

b. Measure each angle. How do the measures compare with your estimates

from part (a)?

2

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name ____________________________________________ Date ____________ Class ____________

Additional Practice (continued)

Shapes and Designs

Investigation 1

A E

B

C D


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3. In the diagram below, the vertical line segment is a diameter of the circle. Use

the diagram and what you know about angle relationships to answer the

following questions.

a. What is the measure of angle 3?

b. The measure of angle 1 is one-fourth of the measure of angle 3. What is the

measure of angle 1?

c. What is the measure of angle 2?

d. The measure of angle 4 is twice the measure of angle 1. What is the

measure of angle 4?

e. What is the measure of angle 5?

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5

Name ____________________________________________ Date ____________ Class ____________


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4. Find each of the angle measures below using an angle ruler or protractor.

a. m�BTA b. m�CTB

c. m�ETB d. m�DTB

e. the complement of m�ETC f. the supplement of m�BTA

AT

E

D

C

B

4


Name ____________________________________________ Date ____________ Class ____________


Shapes and Designs

Investigation 1

AT

E

D

C

B


Name ____________________________________________ Date ____________ Class ____________


Shapes and Designs

5

Draw the polygons described. If there is more than one (or no) shape that you candraw, explain how you know that.

5. Draw a triangle SRT. Side � 3 inches. Side � 3 inches. m�TRS � 120°.

6. Draw a parallelogram ABCD. m�CBA � 75° and m�BAD � 40°.

7. Draw a triangle ABC. Side � 12 centimeters. Side � 6 centimeters.

Side � 20 centimeters.

8. Draw an isosceles trapezoid JKLM. m�JKL � 60° and m�KLM � 120°.

Side � 2 inches and side � 2 inches.KLJK

CABCAB

RTSR

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Name ____________________________________________ Date ____________ Class ____________

Additional Practice: Digital AssessmentsShapes and Designs

Investigation 1

9. Jose drew this shape. What is true regarding

his shape? Select all that apply.

B

CA

n The shape is a polygon.

n Angle A is acute.

n Angle B is acute.

n Angle A is complementary to angle B.

n Angle B is supplementary to angle C.

10. Determine each angle measure using an

angle measuring tool and the values from

the bank. Values may be used more than

once.

95° 100° 105° 110° 120°

125° 130° 135° 140° 180°

11. Write the letter of each angle in the correct box.

A B D E FC

Acute Angle Obtuse Angle Right Angle

000200010271960393_PSA_Unit1_Inv1-3_p001-003.indd 6 08/12/15 10:09 AM

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Investigation 1

Name ____________________________________________ Date ____________ Class ____________

Skill: PolygonsShapes and Designs

1. Tell whether each figure is a polygon. Explain how you know.

a. b.

c. d.

e. f.

Copy

right

© Pe

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its af

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Righ

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d.


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2. Tell whether each figure is a polygon. Explain how you know.

a. b.

c. d.

e. f.

Investigation 1

Name ____________________________________________ Date ____________ Class ____________

Skill: Polygons (continued)

Shapes and Designs


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Name ____________________________________________ Date ____________ Class ____________

Skill: AnglesShapes and Design

Estimate the measure of each angle. Then check your answer with an angle ruler or a protractor.

1. 2.

3. 4.

5. 6.

Draw an angle for each measure.

7. 165° 8. 25°

9. 80° 10. 112°


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Investigation 2

Name ____________________________________________ Date ____________ Class ____________


Answer parts (a) and (b) for each polygon shown in Exercises 1–6.

a. Is the shape a regular polygon? Explain why or why not.

b. Could the shape be used to tile a surface? Make a sketch to demonstrate

your answer.

1. 2.

3. 4.

5. 6.


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Investigation 2Co

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7. The shape below is composed of four polygons.

a. Describe the four polygons in the shape.

b. Can the shape be used to tile a surface? Make a sketch to demonstrate

your answer.

Name ____________________________________________ Date ____________ Class ____________


Shapes and Designs


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Investigation 2

8. An isosceles triangle has two 50° angles. What is the measure of the third

angle? Explain how you found your answer.

9. One angle of an isosceles triangle measures 100°. What are the measures of

the other two angles? Explain your reasoning.

10. Two of the angles of a parallelogram each measure 75°. What are the

measures of the other two angles? Explain your reasoning.

11. One angle of a parallelogram measures 40° and another angle measures

140°. What are the measures of the other two angles? Explain how you

found your answer.

Name ____________________________________________ Date ____________ Class ____________


Shapes and Designs


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12. Can a parallelogram have two 45° angles and two 75° angles? Why or why not?

13. For each of the shapes below, find the unknown angle measure without using

your angle ruler.

a. b.

c. d.

Name ____________________________________________ Date ____________ Class ____________


Shapes and Designs

x

x

120�

120� x

135� 15�

x100�

75�

110�

x x

x


14


Name ____________________________________________ Date ____________ Class ____________


Investigation 2

14. An isosceles triangle has two angles

measuring 40°. Use the tiles below to write

an equation to find the measure of the

third angle.

40 50 180 360

1 2 3 4

5

15. Use values from the bank to label the

missing angle measures.

48° 77° 103° 107° 119° 128° 138°

16. Which of these objects can be used to tile a surface? Write the letter of each shape in the

correct box.

61�

42�

A B D EC

Can Tile a Surface Cannot Tile a Surface


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Find the measure of each angle labeled x.

1. 2. 3.

4. 5. 6.

Find the measure of each angle labeled x.

7. 8. 9.

30�

25�

x

51�

62� x

23�

121�x

74�

53�x54�54�

x 50�

80�

x

71� 48�

108� x98�

54�

130�

149�x 43� x

Name ____________________________________________ Date ____________ Class ____________

Skill: Angle Sums and Exterior Angles of PolygonsShapes and Designs


16


Investigation 2

Find the measure of angle 1 in each figure.

10. 11.

12. 13.

14. 15.

Name ____________________________________________ Date ____________ Class ____________

Skill: Angle Sums and Exterior Angles of PolygonsShapes and Designs

65�

60�1 55� 39�30�

1

111�

68�75�

1

37�

93�

36� 151�

79� 1

61�

40�

46�

1 44�

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Name ____________________________________________ Date ____________ Class ____________


1. A quadrilateral has two sides of length 6. The sum of the lengths of the other

two sides is 15. Use this information to answer the following questions.

a. Suppose the two sides of length 6 are right next to each other. What might

the lengths of the other two sides be? Explain your reasoning.

b. Suppose the quadrilateral is a rectangle and the two sides of length 6 are

opposite each other. What would the lengths of the other two sides have to

be? Explain how you found your answer.

c. Could the quadrilateral have two sides of length 6, one side of length 13.5,

and one side of length 1.5? Explain why or why not.

2. Bob has sketched an equilateral triangle. The sum of the lengths of the sides is

12. What is the length of each side of Bob’s triangle? Explain your reasoning.


18


Investigation 3

3. Angela has sketched a rectangle. She says that the lengths of the sides of the

rectangle add to 26, and the length of one side is 7. What are the length and

width of Angela’s rectangle? Explain how you found your answer.

4. Use the triangle to answer

the following questions.

a. Alex estimates that the unknown side length is about 4.5. How do you

think Alex’s estimate compares with the actual length? Explain your

reasoning.

b. Jennifer estimates that the unknown side length is about 8. How do you

think Jennifer’s estimate compares with the actual length? Explain.

c. Use what you have learned about making triangles with polystrips to

estimate the length of the unknown side. Explain why you think your

estimate is close to the actual length.

Name ____________________________________________ Date ____________ Class ____________


Shapes and Designs

5

2.5


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5. The figure below is made up of squares and triangles. Use the design below and

what you know about angle relationships to answer the following questions.

a. If the measure of angle 1 is 25°, what is the measure of angle 2? Explain

your reasoning.

b. If the measure of angle 1 is 25°, what is the measure of angle 3? Explain

your reasoning.

c. If the measure of angle 1 is 25°, what is the measure of angle 4? Explain

your reasoning.

2

34

2

4

1

1

Name ____________________________________________ Date ____________ Class ____________


Shapes and Designs


20


Name ____________________________________________ Date ____________ Class ____________


Investigation 3

6. In the figure below, two congruent triangles

are embedded in squares. Which statements

are true? Select all that apply.

65�

232 11

65�

n Angle 2 measures 65°.

n Angle 1 measures 65°.

n The measure of angle 3 is equal to the

measure of angle 2.

n The measure of angle 1 is equal to the

measure of angle 2.

n The measure of angle 3 is 70°.

n The measure of angle 1 is 70°.

7. Two parallel lines are cut by a transversal.

Use the values in the bank to label the

measure of each missing angle.

15° 25° 75° 95° 105° 110°

8. Write the letter of each shape in the appropriate category. Shapes may belong to more than

one category.

L2L1

75�

A B D E FC

Rotational Symmetry Reflectional Symmetry


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Tell whether each figure has reflectional symmetry. If it does, draw the line(s) ofsymmetry. If not, write none.

1. 2. 3.

4. 5. 6.

Is there a line of symmetry for each word? If so, draw it.

7. 8.

9. 10.

Name ____________________________________________ Date ____________ Class ____________

Skill: Reflectional SymmetryShapes and Designs

B O X T O O T

M O MC H I C O

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Investigation 3

Tell whether each figure has rotational symmetry. If it does, tell how many timesthe figure fits onto itself in one full turn. If not, write no.

1. 2. 3.

4. 5. 6.

7. 8 9.

Name ____________________________________________ Date ____________ Class ____________

Skill: Rotational SymmetryShapes and Designs


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In each diagram below, lines L1 and L2 are parallel lines cut by a transversal.Find the measure of each numbered angle.

1. 2. 3.

4. Use the figure below. Is line L1 parallel to line L2? Explain how you could use

an angle ruler to support your conjecture.

Name ____________________________________________ Date ____________ Class ____________

Skill: Angles and Parallel LinesShapes and Designs

1

2 3

4

95°

L2

L1

1

23

4 60°

L2L1

1 2

3 4

L2L1

1 3

7

4 2

56 8L2

L1


Documents

000200010271960393 Unit1 Inv1-3 p001-023.qxd 11/21/15 4:25 ...gms7math.weebly.com/uploads/9/2/6/0/9260091/cmp3... · 17 Investigation 3 Copyright © Pearson Education, Inc., or its