# 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 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**, **corresponding angles**, and **alternate angles**. By Euclid's parallel postulate, if the two lines are parallel, consecutive interior angles are supplementary, corresponding angles are equal, and alternate angles are equal.

## Angles of a transversal

A transversal produces 8 angles, as shown in the graph at the above left:

4 with each of the two lines, namely α, β, γ and δ and then α_{1}, β_{1}, γ_{1} and δ_{1}; and
4 of which are **interior** (between the two lines), namely α, β, γ_{1} and δ_{1} and 4 of which are **exterior**, namely α_{1}, β_{1}, γ and δ.
A transversal that cuts two parallel lines at right angles is called a **perpendicular transversal**. In this case, all 8 angles are right angles