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Vocabulary

Review

Parallel Lines and Triangles3-5

Chapter 3 74

Identify the part of speech for the word alternate in each sentence below.

1. You vote for one winner and one alternate.

2. Your two friends alternate serves during tennis.

3. You and your sister babysit on alternate nights.

4. Write the converse of the statement.

Statement: If it is rainingit is raining, then I need an umbrella.

Converse:

Vocabulary Builder

tri- (prefi x) try

Related Word: triple

Main Idea: Tri- is a prefix meaning three that is used to form compound words.

Examples: triangle, tricycle, tripod

Use Your Vocabulary

Write T for true or F for false.

5. A tripod is a stand that has three legs.

6. A triangle is a polygon with three or more sides.

7. A triatholon is a race with two events — swimming and bicycling.

8. In order to triple an amount, multiply it by three.

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Problem 1

Postulate 3-2 Parallel Postulate

Theorem 3-11 Triangle Angle-Sum Theorem

HSM11_GEMC_0305_T93322

C

BA

100° 30°

HSM11_GEMC_0305_T93323

N

M

L

45°

P

hsm11gmse_0305_t00264

A C

B

Dz

4943

59

x y

hsm11gmse_0305_t00267

75 Lesson 3-5

Using the Triangle Angle-Sum Theorem

Got It? Use the diagram at the right. What is the value of z?

Complete each statement.

12. m/A 5

13. m/ABC 5 1 5

14. m/A 1 m/ABC 1 m/C 5

1 1 z 5

z 5 2 2 5

Check your result by solving for z another way.

15. Find m/BDA. 16. Then find m/BDC .

17. Use your answers to Exercises 15 and 16 to find the value of z.

Through a point not on a line, there is one and only one line parallel to the given line.

9. You can draw line(s) through P parallel to line /.

The sum of the measures of the angles of a triangle is 180.

Find each angle measure.

10. 11.

m/C 5 m/L 5

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Problem 2

HSM11_GEMC_0305_T93324

1

2

3

HSM11_GEMC_0305_T93330

1

3

1

3

2

HSM11_GEMC_0305_T93321

46

5

HSM11_GEMC_0305_T93325

HSM11_GEMC_0305_T93326

Triangle Angle-Sum

Exterior AngleExterior AngleExterior Angle

53 + 53 + a =

a =

=

–

y = a +

=

=

+

x = a +

=

=

+

z =

=

+

Chapter 3 76

Using the Triangle Exterior Angle Theorem

Got It? Two angles of a triangle measure 53. What is the measure of an exterior angle at each vertex of the triangle?

21. Use the diagram at the right.

Label the interior angles 538, 538, and a.

Label the exterior angles adjacent to the 538 angles as x and y. Label the third exterior angle z.

22. Complete the flow chart.

An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side. For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles.

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

18. 5 m/2 1 m/3

Circle the number of each exterior angle and draw a box around the number of each remote interior angle.

19. 20.

Theorem 3-12 Triangle Exterior Angle Theorem

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Math Success

Now Iget it!

Need toreview

0 2 4 6 8 10

Problem 3

80

30x

B

D

A

C

Lesson Check

1

3

2 4

Triangle Angle-Sum Theorem

m 1 m 3 m 4

Linear Pair Postulate m 2 180

m 2 180

77 Lesson 3-5

Check off the vocabulary words that you understand.

exterior angle remote interior angles

Rate how well you can use the triangle theorems.

Applying the Triangle Theorems

Got It? Reasoning Can you find mlA without using the Triangle Exterior Angle Theorem? Explain.

23. /ACB and /DCB are complementary / supplementary angles.

24. Find m/ACB.

25. Can you find m/A if you know two of the angle measures? Explain.

__________________________________________________________________________________

• Do you UNDERSTAND?

Explain how the Triangle Exterior Angle Theorem makes sense based on the Triangle Angle-Sum Theorem.

26. Use the triangle at the right to complete the diagram below.

27. Explain how the Triangle Exterior Angle Theorem makes sense based on the Triangle Angle-Sum Theorem.

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