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## GOAL

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**3.4**Proving Lines are Parallel PROVING LINES ARE PARALLEL 1 GOAL 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.**EXAMPLE 1**POSTULATE Corresponding Angles Converse THEOREMS Alternate Interior Angles Converse Consecutive Interior Angles Converse Alternate Exterior Angles Converse**m**p 1 q 2 EXAMPLE 2 Extra Example 1**B**4 A 5 6 D C EXAMPLE 3 Extra Example 2**m**n Find the value of x that makes Extra Example 3**c**d 1 j 4 5 k Checkpoint Given: are supplementary; are supplementary. Prove:**3.4**Proving Lines are Parallel 2 GOAL EXAMPLE 4 EXAMPLE 5 USING THE PARALLEL CONVERSES**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.**155°**D C 65° 40° 65° A B Extra Example 5**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.