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Proving Lines Are Parallel: Theorems & Examples

Explore how to prove lines are parallel using converse postulates and theorems. Examples and checkpoints included for clarity.

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Proving Lines Are Parallel: Theorems & Examples

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  1. 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.

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

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

  4. B 4 A 5 6 D C EXAMPLE 3 Extra Example 2

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

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

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

  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. 155° D C 65° 40° 65° A B Extra Example 5

  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?

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