Use the following figure to answer questions 6-14.

6. Which of the following angles is an alternate interior angle of ?

7. Which of the following angles is an alternate exterior angle of ?

8. Which of the following angles is a corresponding angle of ?

9. If , find .

10. If , find .

- 67°
- 77°
- 109°
- 138°

11. If , find .

- 67°
- 71°
- 109°
- 113°

12. Which of the following statements proves that ?

- 42°
- 67°
- 71°
- 109°

13. Which of the following statements proves that ?

14. If and , then we may conclude that

15. Which theorem guarantees that the lines are parallel in the following construction?

- and will intersect on the left
- and will intersect on the right

- Theorem 3.1.
If alternate interior angles are congruent, then the lines are parallel.- Theorem 3.2.
If corresponding angles are congruent, then the lines are parallel.- Theorem 3.3.
If alternate exterior angles are congruent, then the lines are parallel.- Theorem 3.4.
If interior angles on the same side of the transversal are supplements, then the lines are parallel.

Complete the proof for Theorem 3.5 by selecting the best statement or reason.

Theorem 3.5.If two lines are perpendicular to the same line, then they are parallel to each other.

16. The best option for reason 2 of the proof is

17. The best option for statement 5 of the proof is

- definition of a right angle
- definition of perpendicular lines
- Theorem 3.1
- Theorem 3.5

18. The best option for reason 6 of the proof is

- is a right angle

19. The best option for statement 7 of the proof is

- definition of a right angle
- definition of perpendicular lines
- Theorem 3.2
- Theorem 3.3

20. The best option for reason 9 of the proof is

- Theorem 3.1
- Theorem 3.2
- Theorem 3.3
- Theorem 3.5