Parallel lines cut by a transversal

When a transversal crosses two parallel lines, it creates eight angles that fall into a small number of predictable relationships. Corresponding angles sit in the same position at each crossing (both top-left, both bottom-right, and so on) and the Corresponding Angles Postulate says they are congruent. Alternate interior angles lie between the two parallel lines, on opposite sides of the transversal, and the Alternate Interior Angles Theorem says they too are congruent; alternate exterior angles are the same idea outside the parallel lines, on opposite sides of the transversal, and are also congruent.

The one pair that behaves differently is same-side (also called consecutive) interior angles: they lie between the parallel lines, on the SAME side of the transversal, and the Same-Side Interior Angles Theorem says they are supplementary, not congruent. Once you know any one of the eight angles, every other angle is either equal to it (matching angle or vertical angle) or its supplement -- there are really only two different measures hiding in the whole figure.