Lines on a plane that never intersect each other are parallel lines. A transversal is a line that crosses parallel lines at different points and forms four angles. If the pairs of interior angles formed are equal, then the lines must be parallel.
Corresponding angles are the two angles that lie on the same side of the transversal. These angles are also known as the supplementary interior angles. The pair of interior angles a and b are corresponding angles because they are on the same side of the transversal. The other two pairs of corresponding angles are c and d, p and q, and r and s. These angles are also supplementary because they add up to 180 degrees.
Alternate interior angles are the angles on either side of the transversal and inside the two lines. These angles are the pairs of alternate interior angles and must be congruent. The pair of alternate interior angles a and c are congruent because they have the same measure.
Outside the two lines are the exterior angles. These are the angles above and below the parallel lines. These are the angles that a person would see if he or she walked between the parallel lines and stood on the ground. The angles above the parallel lines are called x-angles and those below the parallel lines are called y-angles. The y-angles must be equal to each other, as must the x-angles.
In this diagram, lines a and b are parallel and they are cut by the transversal at point G. The resulting pair of angles is ABCD and EFCD. These pairs of angles must be equal to each other, as must all corresponding and alternate interior angles in parallel lines.