If two lines are cut by a transversal so that the alternate interior angles are congruent, then these lines are parallel.

Given:
Lines n and m and transversal t


 PROVE: n||m

 PROOF:

 - Given

 -  If two lines intersect, then the vertical angles formed are congruent.

 - Transitive Property of Congruence

m||n - If two lines (m, n) are cut by a transversal (t) so that the corresponding angles () are congruent, then these lines are parallel