1. GOAL 1 PROVING LINES ARE PARALLEL The postulate and theorems learned in Section 3.3 all had the same hypothesis: Parallel lines are cut by a transversal. Now we will prove the converses to be true, and use them to prove lines are parallel. 3.4 Proving Lines are Parallel

2. POSTULATE Corresponding Angles Converse THEOREMS Alternate Interior Angles Converse Consecutive Interior Angles Converse Alternate Exterior Angles Converse EXAMPLE 1

3. Extra Example 1 EXAMPLE 2 1 2 m p q

4. Extra Example 2 EXAMPLE 3 AB CD 6 4 5

5. Extra Example 3 Find the value of x that makes mn

6. Checkpoint Given: are supplementary; are supplementary. Prove: cd j k 5 4 1

7. GOAL 2 USING THE PARALLEL CONVERSES EXAMPLE 4EXAMPLE 5 3.4 Proving Lines are Parallel

8. Extra Example 4 You notice that when your windshield wipers on your car stopped they each made a 30° angle with the bottom of the windshield. If the wipers were long enough, would they ever cross each other? Explain.

9. Extra Example 5 155° 65°40° 65° AB CD

10. Checkpoint 1. When lines r and s are cut by a transversal, are same side interior angles. If is three times, can line r be parallel to line s? Explain.

11. QUESTIONS?