1. 3.3 – Proves Lines are Parallel
What is the definition of a converse?
Is the converse of a true conditional statement always true?

2. 3.3 – Proves Lines are Parallel
Postulate 16 – Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

3. 3.3 – Proves Lines are Parallel
Example 1: Apply the Corresponding Angles Converse
Find the value of y that makes a // b.

4. 3.3 – Proves Lines are Parallel
What is the difference between what you can prove with the Corresponding Angles Converse and the Corresponding Angles Postulate?

5. 3.3 – Proves Lines are Parallel
Theorem 3.4 – Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.

6. 3.3 – Proves Lines are Parallel
Theorem 3.4 – Alternate Exterior Angles Converse
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.

7. 3.3 – Proves Lines are Parallel
Theorem 3.4 – Consecutive Interior Angles Converse
If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.

8. 3.3 – Proves Lines are Parallel
Example 2:
Can you prove that lines a and b are parallel?
Explain why or why not?

9. 3.3 – Proves Lines are Parallel
Example 3: Prove that if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.

10. 3.3 – Proves Lines are Parallel
Example 4: In the figure, a // b and <1 is congruent to <3. Prove c // d. Use a two column or paragraph proof.

11. 3.3 – Proves Lines are Parallel
Theorem 3.7 – Transitive Property of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other.

12. 3.3 – Proves Lines are Parallel
Example 5: Use the Transitive Property of Parallel Lines
In the figure each rung of the ladder is parallel to the rung directly above it. Explain why the top rung is parallel to the bottom rung.