If two lines are cut by a transversal so that the exterior angles on the same side of the transversal are supplementary, then these lines are parallel.

Given:
Lines n and m; transversal t
 

Prove : m||n

Proof:


1: - Given

2: - If the exterior sides of two adjacent angles form a straight line, these angles are supplementary

3: - From 1 and 2

m||n - If two lines (m, n) are cut by a transversal (t) so that the corresponding angles (1, 2) are congruent, then these lines are parallel