1. 3.2 – Proving Lines Parallel1 2 m
Postulate 3-2: Converse of Corresponding Angles Postulate:
If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

2. Proving Lines Parallel1 4 2 m
Theorem 3-5: Converse of Alternate Interior Angles Theorem
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

3. Proof of Theorem 3-5 (C of AIAT)l 3 1 m 2
Statements
Reasons 1. 2. 3. 4.

4. Proving Lines Parallel1 4 2 m
Theorem 3-6: Converse of 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.

5. Proving Lines Parallel

6. Proving Lines Parallel1 b 3 2
Theorem 3-7: Converse of Alternate Exterior Angles Theorem
If two lines and a transversal intersects form alternate exterior angles that are congruent, then the two lines are parallel.

7. Proof of Theorem 3-7 (C of AEAT)1 4 b 2
Statements
Reasons 1. 2. 3. 4.

8. Proving Lines Parallel1 b 3 2
Theorem 3-8: Converse of Same-Side Exterior Angles Theorem
If two lines and a transversal intersects form same-side exterior angles that are supplementary, then the two lines are parallel.

9. Let’s Apply What We Have Learned, K?
Find the value of x for which l || m l
40° m
(2x + 6)°

10. You Try One!
Find the value of x for which a || b a
(7x - 8)° b
62°

11. Homework #12
Pg 137 #1-8, 10-21, 26, 28, 30