3.5 Showing Lines are Parallel

Converse• The converse of an if-then statement is the statement formed by switching the hypothesis and the conclusion.

• 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 is not always necessarily true!

Example 1:Statement: If two segments are congruent, then the two segments have the same length.a) Write the converse of the true statement above.

b) Determine whether the converse is true.

You Try It…Write the converse of the true statement. Then determine whether the converse is true.1) If two angles have the same measure, then the two

angles are congruent.

2) If <A and <B are complementary, then <A + <B = 90.

3) If <C and <D are right angles, then <C = <D.

Corresponding Angles Converse

• We know that if 2 lines are parallel, then corresponding angles are congruent.

• The converse is also TRUE!

• Any time we have corresponding angles that are congruent, we know the lines are parallel.

Example 2:

You Try It…

The converses for our other theorems are ALSO TRUE!

• If alternate interior angles are congruent, lines are parallel.

• If alternate exterior angles are congruent, lines are parallel.

• If same-side interior angles are supplementary, lines are parallel.

Example 3

Example 4

You Try It…

Partner Practice: