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Geometry Section 3-5 1112

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Geometry Section 3-5 1112

  1. 1. Section 3-5 Proving Lines ParallelWednesday, January 4, 2012
  2. 2. Essential Questions • How do you recognize angle pairs tha occur with parallel lines? • How do you prove that two lines are parallel using angle relationships?Wednesday, January 4, 2012
  3. 3. Postulates & Theorems 1. Converse of Corresponding Angles PostulateWednesday, January 4, 2012
  4. 4. Postulates & Theorems 1. Converse of Corresponding Angles Postulate If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.Wednesday, January 4, 2012
  5. 5. Postulates & Theorems 2. Parallel PostulateWednesday, January 4, 2012
  6. 6. Postulates & Theorems 2. Parallel Postulate If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.Wednesday, January 4, 2012
  7. 7. Postulates & Theorems 3. Alternate Exterior Angles ConverseWednesday, January 4, 2012
  8. 8. Postulates & Theorems 3. Alternate Exterior Angles Converse If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel.Wednesday, January 4, 2012
  9. 9. Postulates & Theorems 4. Consecutive Interior Angles ConverseWednesday, January 4, 2012
  10. 10. Postulates & Theorems 4. Consecutive Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.Wednesday, January 4, 2012
  11. 11. Postulates & Theorems 5. Alternate Interior Angles ConverseWednesday, January 4, 2012
  12. 12. Postulates & Theorems 5. Alternate Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel.Wednesday, January 4, 2012
  13. 13. Postulates & Theorems 6. Perpendicular Transversal ConverseWednesday, January 4, 2012
  14. 14. Postulates & Theorems 6. Perpendicular Transversal Converse In a plane, if two lines are perpendicular to the same line, then they are parallel.Wednesday, January 4, 2012
  15. 15. Example 1 Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. a. ∠1≅ ∠3Wednesday, January 4, 2012
  16. 16. Example 1 Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. a. ∠1≅ ∠3 a  b since these congruent angles are also corresponding, the Corresponding Angles Converse holdsWednesday, January 4, 2012
  17. 17. Example 1 Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. b. m∠1= 103° and m∠4 = 100° ∠1 and ∠4Wednesday, January 4, 2012
  18. 18. Example 1 Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. b. m∠1= 103° and m∠4 = 100° ∠1 and ∠4 are alternate interior angles, but not congruent, so a is not parallel to cWednesday, January 4, 2012
  19. 19. Example 2 Find m∠ZYN so that PQ  MN.Wednesday, January 4, 2012
  20. 20. Example 2 Find m∠ZYN so that PQ  MN. 11x − 25 = 7x + 35Wednesday, January 4, 2012
  21. 21. Example 2 Find m∠ZYN so that PQ  MN. 11x − 25 = 7x + 35 4x = 60Wednesday, January 4, 2012
  22. 22. Example 2 Find m∠ZYN so that PQ  MN. 11x − 25 = 7x + 35 4x = 60 x = 15Wednesday, January 4, 2012
  23. 23. Example 2 Find m∠ZYN so that PQ  MN. 11x − 25 = 7x + 35 4x = 60 x = 15 m∠ZYN = 7(15) + 35Wednesday, January 4, 2012
  24. 24. Example 2 Find m∠ZYN so that PQ  MN. 11x − 25 = 7x + 35 4x = 60 x = 15 m∠ZYN = 7(15) + 35 = 105 + 35Wednesday, January 4, 2012
  25. 25. Example 2 Find m∠ZYN so that PQ  MN. 11x − 25 = 7x + 35 4x = 60 x = 15 m∠ZYN = 7(15) + 35 = 105 + 35 = 140Wednesday, January 4, 2012
  26. 26. Example 2 Find m∠ZYN so that PQ  MN. 11x − 25 = 7x + 35 4x = 60 x = 15 m∠ZYN = 7(15) + 35 = 105 + 35 = 140 m∠ZYN = 140°Wednesday, January 4, 2012
  27. 27. Check Your Understanding Review problems #1-7 on page 208Wednesday, January 4, 2012
  28. 28. Problem SetWednesday, January 4, 2012
  29. 29. Problem Set p. 209 #9-27 odd, 37 “Nothing in life is to be feared. It is only to be understood.” - Marie CurieWednesday, January 4, 2012

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