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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