Thread: Parallel Lines.

Use the following figure to answer questions 6-14.

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

1. 
2. 
3. 
4. 

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

1. 
2. 
3. 
4. 

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

1. 
2. 
3. 
4. 

9. If , find .

1. 67°
2. 77°
3. 109°
4. 138°

10. If , find .

1. 67°
2. 71°
3. 109°
4. 113°

11. If , find .

1. 42°
2. 67°
3. 71°
4. 109°

12. Which of the following statements proves that ?

1. 
2. 
3. 
4. 

13. Which of the following statements proves that ?

1. 
2. 
3. 
4. 

14. If and , then we may conclude that

1. 
2. 
3. and will intersect on the left
4. and will intersect on the right

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

1. Theorem 3.1. If alternate interior angles are congruent, then the lines are parallel.
2. Theorem 3.2. If corresponding angles are congruent, then the lines are parallel.
3. Theorem 3.3. If alternate exterior angles are congruent, then the lines are parallel.
4. 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

1. definition of a right angle
2. definition of perpendicular lines
3. Theorem 3.1
4. Theorem 3.5

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

1. is a right angle
2. 
3. 
4. 

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

1. definition of a right angle
2. definition of perpendicular lines
3. Theorem 3.2
4. Theorem 3.3

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

1. 
2. 
3. 
4. 

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

1. Theorem 3.1
2. Theorem 3.2
3. Theorem 3.3
4. Theorem 3.5

Pleaaaase, tell us where you have problems only...
Imagine if we have to justify each answer...

Why don't you start by telling us where you are having the problems. Solving the whole sheet probably won't do you any good otherwise since many of the solutions here are from the definitions.

-Dan