Parallel and Perpendicular Lines Chapter 3 Parallel and Perpendicular Lines

Section 5 Showing Lines are Parallel

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.

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.

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.

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

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

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

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

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

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

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