1. Congruent Angles Associated with Parallel Lines

2. Parallel Postulate: Through a point not on a line, there is exactly one parallel to the given line. a P

3. Notice the special tick marks ( ) used to designate parallel lines.

5. Six Theorems About Parallel Lines

11. If two parallel lines are cut by a transversal, then Each pair of alternate interior angles are congruent Each pair of alternate exterior angles are congruent Each pair of corresponding angles are congruent Each pair of interior angles on the same side of the transversal are supplementary Each pair of exterior angles on the same side of the transversal are supplementary.

12. Since alt. int.  s are , 3x + 5 = 2x + 10 x + 5 = 10 x = 5 3(5) + 5 = 20 Because vertical  s are , m  1 = 20.

13. 1.FA ║ DE 2.  A   D 3.FA  DE 4.AB  CD 5.AC  BD 6.ΔFAC  ΔEDB 7.  F   E 1.Given 2.║ lines → alt. int.  s  3.Given 4.Given 5.Addition Property (BC to step 4) 6.SAS (3, 2, 5) 7.CPCTC

14. Using the Parallel Postulate, draw m parallel to a.  2 &  3 are congruent (alt. int.  s are  )  3 = 40°  4 &  5 are supplementary.  4 = 80°  1 = 40° + 80° = 120° m 4 3 2 5