1. 3.2 – Use Parallel Lines and Transversals
Postulate 15 – Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

2. 3.2 – Use Parallel Lines and Transversals
Example 1: Identify congruent angles
The measure of three of the numbered angles is 55 degrees. Identify the angles. Explain your reasoning.
What are the measures of the
other angles in the picture?

3. 3.2 – Use Parallel Lines and Transversals
Theorem 3.1 – Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

4. 3.2 – Use Parallel Lines and Transversals
Theorem 3.1 – Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

5. 3.2 – Use Parallel Lines and Transversals
Theorem 3.1 – Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

6. 3.2 – Use Parallel Lines and Transversals
Example 2 – Use properties of parallel lines
Find the value of x.

7. 3.2 – Use Parallel Lines and Transversals
Example 3 – Use properties of parallel lines
Find the value of x.

8. 3.2 – Use Parallel Lines and Transversals
Example 4 – Use properties of parallel lines
Find the value of x.

9. 3.2 – Use Parallel Lines and Transversals
Example 5 – Use properties of parallel lines
Find the value of x and y.

10. 3.2 – Use Parallel Lines and Transversals
Example 6 – Use properties of parallel lines
Find the value of x and y.

11. 3.2 – Use Parallel Lines and Transversals
Example 7 – Use properties of parallel lines
Find the value of x and y.

12. 3.2 – Use Parallel Lines and Transversals
Example 8 – Prove the Alternate Interior Angles Theorem
Prove that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

13. 3.2 – Use Parallel Lines and Transversals
Example 9 – Solve a real world problem.
When sunlight enters a drop of rain, different colors of light leave the drop at different angles. This process is what makes a rainbow. For violet light, m<2 = 40 degrees. What is m<1? How do you know?