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

l m If 1 2, then l m. 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. 1 l l m m 2 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. If 1 2, then l m. l 1 4 m 2

If 2 and 4 are supplementary, then l m 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 1 4 m 2

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

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

Example 3: Which lines, if any, must be parallel if 3 4? Justify your answer with a theorem or postulate. 3 EC is parallel to DK by Postulate 3-2, Converse of Corresponding Angles Postulate. E C D 1 4 K 2

Assignment: pg.125-128 #1-15;27-35;40-44