1. Chapter 3 Lesson 2 Objective: Objective: To use a transversal in proving lines parallel.

2. Postulate 3-2: Converse of the Corresponding Angles Postulate If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. Theorem 3-3: Converse of the Alternate Interior Angles Theorem If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. l m 1 2 l m l m 1 2 4 If 1 2, then l m.

3. Theorem 3-4: Converse of the Same-Side Interior Angles Theorem If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. If 2 and 4 are supplementary, then l m l m 1 2 4

4. Example 1: Proving Theorem 3-3 StatementsReasons 1.) 2.) 3.) 4.) Given: 1 2 Prove: l m l m 1 2 3 1 2 1 3 3 2 l m Given Vertical angles are congruent Transitive Prop. Of Congruence Postulate 3-2

5. Example 2: Using Theorem 3-4 Which lines, if any, must be parallel if 1 2? Justify your answer with a theorem or postulate. E D C K1 3 4 2 DE is parallel to KC by Theorem 3-3, the Converse of Alternate Interior Angles Theorem.

6. Example 3: Which lines, if any, must be parallel if 3 4? Justify your answer with a theorem or postulate. E D C K1 3 4 2 EC is parallel to DK by Postulate 3-2, Converse of Corresponding Angles Postulate.

7. Example 4: Proof of Theorem 3-6 StatementsReasons 1.) 2.) 3.) 4.) r s 5.) r s 4.) 5.) Given: Prove: r s s r Given All Right Angles are Congruent Converse of Corresponding Angles Postulate t 1 2 Angles 1 & 2 are right angles Definition of Perpendicular lines

8. l m (2x+6) 40 Example 5: Find the value of x for which l m. Corresponding Angles 2x+6 = 40 2x=34 x=17

9. Assignment: pg.125-127 #1-35 DUE Monday