Conditions for Parallel Lines
The conditions that guarantee that lines are parallel are enumerated in the following postulate and theorems. These theorems that will help you prove that two lines are parallel are the converses of the Corresponding Angles Postulate (CAP), Alternate Interior Angles Theorem, Alternate Exterior Angles Theorem, Same-Side Interior Angles Theorem, and Same-Side Exterior Angles Theorem.
Postulate. Converse of CAP
If two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are parallel.
Refer to the given figure. If corresponding angles 1 and 5 are congruent, then lines m and n are parallel.
