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Skills Practice Skills Practice for Lesson 13.1

Name _____________________________________________ Date _________________________

Replacement for a Carpenter’s SquareInscribed Polygons

Vocabulary Define each term in your own words.

1. polygon inscribed in a circle

Problem Set Draw a triangle inscribed in the circle through the three points. Then determine if the triangle is a right triangle.

2. A

BC

O

3.

A

B

C

O

4. A

B

C

O

5. A

B

C

O

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6. A

C

B

O

7.

C

A

B

O

8.

C

A

B

O

9.

C

A

B

O

Draw a quadrilateral inscribed in the circle through the four points. Then, determine the measure of the given angle.

10. If mADC � 190°, calculate m�ADC.

C

D

A

B

�

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11. If mABC � 220°, calculate m�ABC.

C

D

A

B

12. If mBAD � 280°, calculate m�BAD.

C

D

A

B

�

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13. If mADC � 310°, calculate m�ADC.

B

D

A

C

14. If mADC � 190° and m�BCD � 100°, calculate m�BAD.

B

D

A

C

�

�

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15. If mBAD � 240° and m�ABC � 105°, calculate m�ADC.

B

D

A

C

16. If ___

AD || ___

BC and mBAD � 260°, calculate m�ADC.

B

D

A

C

�

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17. If mBAD � 180° and �BCD and �ADC are supplementary angles, calculate m�ABC.

B

D

A

C

�

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Write a two-column proof to prove each statement.

18. Given: mAB � 50°, mBC � 90°, and mCD � 90°

Prove: m�BCD � 90°

B

D

A

C

� � �

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19. Given: �BAD and �ADC are supplementary angles

Prove: m�BAD � m�ABC

B

C

A

D

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20. Given: mABC � 180° and mBCD � 180°

Prove: Quadrilateral ABCD is a rectangle

B

O

A

D

C

� �

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21. Given: mAB � mBC � mCD � mDE � mAE � 72°

Prove: ABCDE is a regular pentagon

C

B

A

E

D

� � � � �

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Skills Practice Skills Practice for Lesson 13.2

Name _____________________________________________ Date _________________________

Box It UpNets

Vocabulary Give an example of each net.

1. net of a triangular pyramid 2. net of a cube

Problem Set Identify the shape of each of the faces of the polyhedron. Then, classify each polyhedron as completely as possible.

3. 4.

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5. 6.

7. 8.

9. 10.

Identify the base(s) of each polyhedron. Then, classify the polyhedron formed by each net.

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11. 12.

13. A triangular prism has a height of 3 centimeters, a width of 2 centimeters, and a length of

4 centimeters.

14. A cube with sides of length 3 centimeters.

Draw a net based on each description. Each grid square represents a square that is 1 centimeter long and 1 centimeter wide.

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15. A square pyramid has a width of 4 centimeters and a height of 3 centimeters.

16. A cylinder has a height of 5 centimeters and a diameter of 3 centimeters.

Use each net to calculate the surface area of each polyhedron. Each grid square represents a square that is 1 centimeter long and 1 centimeter wide. Use 3.14 for � and round to the nearest hundredth when necessary.

17.

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18.

19.

20.

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Skills Practice Skills Practice for Lesson 13.3

Name _____________________________________________ Date _________________________

Tree RingsCross Sections

Vocabulary

Match each word with its definition.

1. a flat figure that extends in all directions a. cross section

2. a two-dimensional figure that is formed by the b. great circle

intersection of the solid and a plane

3. a cross section of a sphere that has the same c. plane

diameter as the sphere

Problem Set Describe the cross section shown in each figure.

4. 5.

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6. 7.

8. 9.

10. 11.

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12. 13.

14. 15.

Describe the vertical and horizontal cross sections of each polyhedron.

16. 17.

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18. 19.

20. 21.

22. 23.

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Skills Practice Skills Practice for Lesson 13.4

Name _____________________________________________ Date _________________________

Minerals and CrystalsPolyhedra and Euler’s Formula

VocabularyWrite the term from the box that best completes each statement. Each word may be used more than once.

regular polygon regular polyhedron cube faces

edges vertices Platonic solids

1. A(n) is a solid that is formed from .

2. The of a polyhedron are the line segments formed by the intersection

of two faces.

3. A regular prism is also called a(n) .

4. The of a polyhedron are the points where three or more edges meet.

5. The five regular polyhedra made from regular triangles, squares, and pentagons are

called .

6. Euler’s Formula says that for a polyhedron the number of plus two is

equal to the number of vertices and .

7. If a pyramid has an n-gon for a base, then it has n � 1 .

8. If a prism has an n-gon for a base, then it has 2n .

Problem Set Determine the number of faces, edges and vertices for each polyhedra.

9. 10.

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11. 12.

13. 14.

15. 16.

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17. 18.

Use Euler’s Formula to answer each question.

19. A regular polyhedron has 12 edges and 6 vertices. How many faces does it have?

20. A regular polyhedron has 4 vertices and 4 faces. How many edges does it have?

21. A polyhedron has 8 faces and 11 vertices. How many edges does it have?

22. A polyhedron has 10 edges and 6 faces. How many vertices does it have?

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Skills Practice Skills Practice for Lesson 13.5

Name _____________________________________________ Date _________________________

Isometric DrawingsCompositions

Vocabulary Define each term in your own words.

1. isometric drawing

2. orthographic projection

3. top view

4. front view

5. side view

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Problem Set Draw the top, front, and side views for each figure.

6.

7.

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8.

9.

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10.

11.

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For each top, front, and side view of a three-dimensional figure, draw an isometric drawing.

12.

Top View Front View Side View

13.

Top View Front View Side View

14.

Top View Front View Side View

15.

Top View Front View Side View

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16.

Top View Front View Side View

17.

Top View Front View Side View