1. Chapter 3.3 Notes: Prove Lines are Parallel
Goal: You will use angle relationships to prove that lines are parallel.

2. Postulate 16 Corresponding Angles Converse:
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Ex.1: Find the value of x that makes m║n.

3. Ex. 2: Is there enough information in the diagram to conclude that m║n
Ex.2: Is there enough information in the diagram to conclude that m║n? Explain.
Theorem 3.4 Alternate Interior Angles Converse:
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

4. Theorem 3.5 Alternate Exterior Angles Converse:
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
Theorem 3.6 Consecutive Interior Angles Converse:
If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

5. Can you prove that lines a and b are parallel? Explain why or why not.
Ex.3: Ex.4:
Ex.5:

6. Ex.6: Find the value of y that makes a║b. (5y+ 6)o 121o

7. Ex.7: Given: Prove: p║q

9. Ex.8: Given: Prove: r || p

10. Ex.9: Given: Prove:

11. Ex.10: Given: Prove: and are supplementary. 1 p 3 2 q

12. Ex.11: Given: are supplementary Prove: l || m

13. Ex.12: Given: Prove: