corresponding angles
When a transversal crosses two lines, each crossing produces the same little fan of four angles. The corresponding angles are the ones in matching positions at the two crossings — for example, the top-right angle at the upper crossing and the top-right angle at the lower crossing. Many learners spot them by the shape of a capital letter F: the two angles tucked into the corners of the F are corresponding.
Precisely: at the upper crossing and the lower crossing, an angle on the same side of the transversal and the same side of its own line (both above-left, or both below-right, and so on) form a pair of corresponding angles. There are four such pairs among the eight angles. The corresponding-angles postulate (for Euclidean geometry) says that if the two crossed lines are parallel, then corresponding angles are equal; and conversely, if a pair of corresponding angles is equal, the two lines are parallel. This converse is one of the standard ways to prove two lines parallel.
Be careful: corresponding angles are equal only when the two crossed lines are parallel. If you slide a transversal across two lines that splay apart, the matching-position angles drift out of step. So an equality of corresponding angles is both a consequence of parallelism and a usable test for it — never assume it without one or the other.
A transversal cuts two parallel lines. At the upper crossing the angle above-right of the line is 72 degrees. The corresponding angle at the lower crossing, also above-right, is therefore 72 degrees.
With parallel lines, corresponding angles are equal (the F-shape).
Corresponding angles are equal only for parallel lines; if the lines are not parallel the matching-position angles differ, so equality is exactly the test for parallelism.