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3.4 Proving Lines are Parallel

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3.4 Proving Lines are Parallel. Mr. Robinson Fall 2011. Essential Question:. How can you prove that 2 lines are parallel?. Postulate 16: Corresponding Angles Converse. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

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3.4 Proving Lines are Parallel
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  1. 3.4 Proving Lines are Parallel Mr. Robinson Fall 2011

  2. Essential Question: How can you prove that 2 lines are parallel?

  3. Postulate 16: Corresponding Angles Converse • If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

  4. Theorem 3.8: Alternate Interior Angles Converse • If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

  5. Theorem 3.9: Consecutive Interior Angles Converse • If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

  6. Theorem 3.10: Alternate Exterior Angles Converse • If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

  7. Solution: Lines j and k will be parallel if the marked angles are supplementary. x + 4x = 180  5x = 180  X = 36  4x = 144  So, if x = 36, then j ║ k. Find the value of x that makes j ║ k. 4x x

  8. Using Parallel Converses:Using Corresponding Angles Converse SAILING. If two boats sail at a 45 angle to the wind as shown, and the wind is constant, will their paths ever cross? Explain

  9. Solution: Because corresponding angles are congruent, the boats’ paths are parallel. Parallel lines do not intersect, so the boats’ paths will not cross.

  10. Example 5: Identifying parallel lines Decide which rays are parallel. H E G 58 61 62 59 C A B D A. Is EB parallel to HD? B. Is EA parallel to HC?

  11. Example 5: Identifying parallel lines Decide which rays are parallel. H E G 58 61 B D • Is EB parallel to HD? mBEH = 58 m DHG = 61 The angles are corresponding, but not congruent, so EB and HD are not parallel.

  12. Example 5: Identifying parallel lines Decide which rays are parallel. H E G 120 120 C A • B. Is EA parallel to HC? m AEH = 62 + 58 m CHG = 59 + 61 AEH and CHG are congruent corresponding angles, so EA ║HC.

  13. Conclusion: Two lines are cut by a transversal. How can you prove the lines are parallel? Show that either a pair of alternate interior angles, or a pair of corresponding angles, or a pair of alternate exterior angles is congruent, or show that a pair of consecutive interior angles is supplementary.

  14. HW ASSIGNMENT: • 3.4--pp. 153-154 #3 - 27