PROPERTIES OF

1. P A R A L L E L P L A N E S I L N E S A N D

2. PROPERTIES OF PARALLEL LINES

3. Objectives: 1. State and apply the postulates and theorems involving the properties of parallel lines; and 2. Solve algebraic and real life problems involving the properties of parallel lines.

4. Corresponding Angles Postulate m // e and cut by a transversal line l. 1 2 m 3 4 6 5 e 7 8 l If two parallel lines are cut by a transversal, then the correspon-ding angles are congruent.

5. ~ Prove: 1 = 2 ~ 3 2. 2 = 3 a ~ 1 3. 3 = 1 2 b ~ 4. 1 = 2 PAI Theorem. If two parallel lines are cut by a transversal, then the alternate interior s are congruent. Given: a ll b Statements: 1. a ll b

6. Example: h 1 2 3 d If h // d, m1 = 30 + x, m2 = 40, m3 = 2x - 100, find m1 and m3.

7. 3 a 2 b 1 PAE Theorem. If two parallel lines are cut by transversal, then the alternate exterior angles are congruent.

8. a 1 3 2 b PSSI Theorem. If two parallel lines are cut by a transversal, then the same-side interior angles are supplementary.

9. 1 3 a b 2 PSSE Theorem. If two parallel lines are cut by a transversal, then the same-side exterior angles are supplementary.

10. Individual Practice: Answer workbook exercise on p. 51-52 (20 points)