I know that if two lines are parallel and there is a transversal crossing both, the alternate interior angles are congruent, alternate exterior angles congruent, etc. etc.
According to the geometry textbook that the student I'm tutoring brought, the converse is true as well: if the alternate interior angles are congruent, or the consecutive interior angles are supplementary, etc., then the lines must be parallel.
Why should this be? I mean, it looks like it should be true, but what is the proof that it's true?