1. Section 3.5 Properties of Parallel Lines

2. Transversal  Is a line that intersects two or more coplanar lines at different points.  Angles formed:  Corresponding angles  Alternate interior angles  Alternate exterior angles  Consecutive interior angles

3. corresponding <1 and <5 <4 and <8 <3 and <7 <2 and <6 Alt interior <3 and <5 <2 and <8 Alt exterior <1 and <7 <4 and <6 Consecutive interior angles <2 and <5 <3 and <8

4. Using properties of Parallel Lines  Postulate 15: Corresponding Angles Postulate  If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

5. Theorem 3.6 Alternate Interior Angles Theorem  If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

6. Given: m ││n Prove: <1 ≌ <2

7. StatementsReasons 1. m││n1. given 2. <3 and <1 are2. def of vert <‘s vertical <‘s 3. <3 ≌ <13. vertical <‘s thm 4. <3 ≌ <24. 2 lines ll corr <‘s are ≌ 5. <1 ≌ <25. transitive prop

8. Theorems:  Thm 3.7: Consecutive Interior Angles Theorem  If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary  Thm 3.8: Alternate Exterior Angles Theorem  If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent  Thm 3.9: Perpendicular Transversal Theorem  If transversal is perpendicular to one of two parallel lines, then it is perp to the second.

9. Parallel Lines and Transversals  Example Given that m  5 = 65°, find each measure. Tell which postulate or theorem you used to find each one. a. b. c. d. 8 6 7 5 9 p q

10. Parallel Lines and Transversals  Example  How many other angles have a measure of 100°? A B C 100° D AB || CD AC || BD

11. Parallel Lines and Transversals  Example  Use properties of parallel lines to find the value of x. (x – 8)° 72°

12. Parallel Lines and Transversals  Example  Find the value of x. (x – 20)° x° 70°