1. 3-2 Properties of Parallel Lines

2. Congruent Angle Relationships
Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding angles are congruent. Alternate Interior Angles Theorem: If a transversal intersects two parallel lines, then alternate interior angles are congruent. Alternate Exterior Angles Theorem: If a transversal intersects two parallel lines, then alternate exterior angles are congruent.

3. Identifying Congruent Angles
Which angles measure 55? How do you know?

4. Proof: Alternate Interior Angles Theorem
Given: l  m Prove: 4  6

5. Other Angle Relationships
Same-Side Interior Angles Theorem: If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

6. Proof: Proving Angles Supplementary
Given: a ll b Prove: 1 and 8 are supplementary

7. Finding Measures of Angles
What are the measures of each angle? Justify each answer.

8. Finding an Angle Measure
What is the value of y?

9. 3-3 Proving Lines Parallel

10. Converses of Postulates and Theorems
Converse of the Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel. 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. Converse of the Same-Side Interior Angles Theorem: If two lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel. Converse of the Alternate Exterior Angles Theorem: If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

11. Identifying Parallel Lines
Which lines are parallel if 1  2? Justify your answer.
Which lines are parallel if 6  7? Justify your answer.

12. Using Algebra
What is the value of x for which a ll b?