Corresponding Angles

The term corresponding angles is often used when two lines are cut by a third line, a transversal.

Two parallel lines cut by a transversal n, with angles labeled 1 through 8

In the figure above, line t is a transversal cutting lines k and l, and there are four pairs of corresponding angles:

1 and 5

2 and 6

3 and 7

4 and 8

The Corresponding Angles Postulate states that if k and l are parallel, then the pairs of corresponding angles are congruent. The converse of this theorem is also true.

The term corresponding angles is also sometimes used when making statements about similar or congruent polygons. For example, in the figure below featuring two similar pentagons, A and V are corresponding angles.

Two Similar Pentagons ABCDE and VWXYZ