Transversal (geometry)

In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two or more other lines in the Euclidean plane are parallel. The intersections of a transversal with two lines create various types of pairs of angles: consecutive interior angles, consecutive exterior angles, corresponding angles, and alternate angles. As a consequence of Euclid's parallel postulate, if the two lines are parallel, consecutive interior angles are supplementary, corresponding angles are equal, and alternate angles are equal.

Eight angles of a transversal. (Vertical angles such as ${\displaystyle \alpha }$ and ${\displaystyle \gamma }$ are always congruent.)		Transversal between non-parallel lines. Consecutive angles are not supplementary.	Transversal between parallel lines. Consecutive angles are supplementary.