Lesson 14. 3: Proving Lines Parallel The converse of a conditional statement, “if p, then q”, is the statement, “if q, then p”. That is, to write the converse of a conditional statement, just interchange the hypothesis and conclusion. Note: The converse of a conditional statement is not necessarily true.

Your Turn Complete the Explore section, parts A through D and Reflect 1 and 2.

Postulate Converse of Same-Side Interior Angles Postulate If two lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the lines are parallel.

Theorems Convers of Alternate Interior Angles Theorem If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel. Converse of Alternate Exterior Angles Theorem If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

One More Theorem Convers of Corresponding Angles Theorem If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

Prove the Converse of the Corresponding Angles Theorem Given: Prove:

The Parallel Postulate Given a line and a point not on the line, exactly on line can be drawn through the point so that it is parallel to the given line. If , then