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

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

3. 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

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

5. Example 2: Using Theorem 3-4
Which lines, if any, must be parallel if ? 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

6. Example 3:
Which lines, if any, must be parallel if ? 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

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