Math II Teachers Skills Practice Chapter 10

Lesson 10.1 Skills Practice

Name

Date

Replacement for a Carpenter's Square

Inscribed and Circumscribed Triangles and Quadrilaterals

Vocabulary

Answer each question.

1. How are inscribed polygons and circumscribed polygons different? Inscribed polygons are drawn inside of a circle with all vertices touching the circle. Circumscribed polygons are drawn outside of a circle with all sides tangent to the circle.

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2. Describe how you can use the Inscribed Right Triangle?Diameter Theorem to show an inscribed triangle is a right triangle.

If an inscribed triangle has one side that is a diameter of the circle, then the triangle must be a right triangle.

3. What does the Converse of the Inscribed Right Triangle?Diameter Theorem help to show in a circle? If a right triangle is inscribed in a circle then one of the sides of the triangle must be the diameter.

4. What information about a quadrilateral inscribed in a circle does the Inscribed Quadrilateral?Opposite Angles Theorem give? If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary.

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Chapter 10 Skills Practice 777

Lesson 10.1 Skills Practice

page 2

Problem Set

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

1.

A

2.

A

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O

C

B

B O

C

No. The triangle is not a right triangle. No. The triangle is not a right triangle. None of the sides of the triangle is a None of the sides of the triangle is a diameter of the circle. diameter of the circle.

3.

A

4.

A

C

B O

O B

C

Yes. The triangle is a right triangle. Yes. The triangle is a right triangle. Line segment AC is a diameter Line segment BC is a diameter of of the circle. the circle.

5.

A B

6. A

O

O

C B

C

Yes. The triangle is a right triangle. Yes. The triangle is a right triangle. Line segment BC is a diameter Line segment AB is a diameter of the circle. of the circle.

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778 Chapter 10 Skills Practice

Lesson 10.1 Skills Practice

page 3

Name

Date

7. A

B

O

C

8.

A

O

B C

No. The triangle is not a right triangle. No. The triangle is not a right triangle. None of the sides of the triangle is a None of the sides of the triangle is a diameter of the circle. diameter of the circle.

Draw a triangle inscribed in the circle through the given points. Then determine the measure of the indicated angle.

9. In ABC, mA 5 55?. Determine mB.

A

10

C

B

mB 5 180? 2 90? 2 55? 5 35?

10. In ABC, mB 5 38?. Determine mA.

C A

B

mA 5 180? 2 90? 2 38? 5 52?

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Chapter 10 Skills Practice 779

Lesson 10.1 Skills Practice

11. In ABC, mC 5 62?. Determine mA.

B

A

C

mA 5 180? 2 90? 2 62? 5 28?

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12. In ABC, mB 5 26?. Determine mC.

C

A B

mC 5 180? 2 90? 2 26? 5 64?

13. In ABC, mC 5 49?. Determine mA.

A

B

C

mA 5 180? 2 90? 2 49? 5 41? 14. In ABC, mB 5 51?. Determine mA.

A C

B

mA 5 180? 2 90? 2 51? 5 39?

780 Chapter 10 Skills Practice

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Lesson 10.1 Skills Practice

page 5

Name

Date

Draw a quadrilateral inscribed in the circle through the given four points. Then determine the measure of the indicated angle. 15. In quadrilateral ABCD, mB 5 81?. Determine mD.

A

B

D C

mD 5 180? 2 81? 5 99?

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16. In quadrilateral ABCD, mC 5 75?. Determine mA.

A B

D C

mA 5 180? 2 75? 5 105?

17. In quadrilateral ABCD, mB 5 112?. Determine mD.

A

B

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D

C

mD 5 180? 2 112? 5 68?

Chapter 10 Skills Practice 781

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