1. Parallel and Perpendicular Lines
Chapter 3
Parallel and Perpendicular Lines

2. Section 5 Showing Lines are Parallel

3. Suppose two lines are cut by a transversal and a pair of corresponding angles are congruent. Are the two lines parallel? This question asks whether the converse of the Corresponding Angles Postulate is true. The __________________________ of an if-then statement is the statement formed by switching the hypothesis and the conclusion. Here is an example. Statement: If you live in Sacramento, then you live in California. Converse: If you live in California, then you live in Sacramento. The converse of a true statement may or may not be true. As shown in the example above, if you live in California, you don’t necessarily live in Sacramento; you could live in Los Angeles or San Diego.

4. Example 1: Write the Converse of an If-Then Statement
Statement: If two segments are congruent, then the two segments have the same length.
Write the converse of the true statement above.
Determine whether the converse is true.

5. Checkpoint: Write the Converse of an If-Then Statement
Write the converse of the true statement. Then determine whether the converse is true.
If two angles have the same measure, then the two angles are congruent.
If <3 and <4 are complementary, then m<3 + m<4 = 90°.
If <1 and <2 are right angles, then <1 ≅ <2.

6. Converse of a Postulate Postulate 9 below is the converse of Postulate 8, the Corresponding Angles Postulate, which we learned in Lesson 3.4.

7. Example 2: Apply Corresponding Angles Converse Is enough information given to conclude that BD || EG? Explain

8. Checkpoint: Apply Corresponding Angles Converse Is enough information given to conclude that RT || XZ? Explain.

10. Example 3: Identify Parallel Lines Does the diagram give enough information to conclude that m || n?

11. Checkpoint: Identify Parallel Lines Does the diagram give enough information to conclude the c || d? Explain.

13. Example 4: Use Same-Side Interior Angles Converse Find the value of x so that j || k.

14. Checkpoint: Use Same-Side Interior Angles Converse Find the value of x so that v || w.