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3.3 Parallel Lines and Transversals

3.3 Parallel Lines and Transversals. Proving angles congruent with parallel lines. Corresponding Angles Postulate. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2 3 4 5 6 7 8 . Alternate Interior Angles.

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3.3 Parallel Lines and Transversals

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  1. 3.3 Parallel Lines and Transversals Proving angles congruent with parallel lines

  2. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2 3 4 5 6 7 8

  3. Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 1 2 3 4 5 6 7 8

  4. Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior interior angles are congruent. 1 2 3 4 5 6 7 8

  5. Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 1 2 3 4 5 6 7 8

  6. Perpendicular Transversal If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. If k // l and k m, k lthen l m. 9 10 11 12 m

  7. Given: p//q Prove: #1. p//q #1. Given3 1 5 6 7 8 4 2

  8. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2. 5 6 7 8 4 2

  9. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2.Linear pairs 5 6 are Supplementary 7 8 4 2

  10. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2.Linear pairs 5 6 are Supplementary 7 8 #3. 4 2

  11. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2.Linear pairs 5 6 are Supplementary 7 8 #3. #3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent.

  12. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2.Linear pairs 5 6 are Supplementary 7 8 #3. #3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.

  13. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2.Linear pairs 5 6 are Supplementary 7 8 #3. #3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4. #4. Def. of congruent

  14. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2.Linear pairs 5 6 are Supplementary 7 8 #3. #3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4. #4. Def. of congruent #5.

  15. Given: p//q Prove: #1. p//q #1. Given3 1 #2. #2.Linear pairs 5 6 are Supplementary 7 8 #3. #3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4. #4. Def. of congruent #5. #5. Substitution

  16. Solve for x 1

  17. Solve for x X

  18. Homework Page 146-148 #8 – 10, 11- 27 odd, 29, 31

  19. Homework Page 146-149 # 12 – 28 even, 33- 44

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