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: vertical angles, consecutive interior angles, consecutive exterior angles, corresponding angles, alternate interior angles, alternate exterior angles, and linear pairs. As a consequence of Euclid's parallel postulate, if the two lines are parallel, consecutive angles and linear pairs are supplementary, while corresponding angles, alternate angles, and vertical 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.