Definition: Corresponding angles occupy the same relative position at two intersections of a transversal; when the lines are parallel, they are congruent.
What are corresponding angles?
At each intersection there are four angles. Pair the top-left at one point with the top-left at the other, the bottom-right with the bottom-right, and so on. That gives four pairs, and the shape of each pair is an F.
What does the postulate say?
If a transversal crosses two parallel lines, then corresponding angles are congruent. Conversely, congruent corresponding angles prove the lines are parallel.
Example. Two lines are cut by a transversal. A top-left angle measures (5x + 9) degrees and the matching top-left angle measures (8x – 21) degrees. If the lines are parallel: 5x + 9 = 8x – 21, so 30 = 3x and x = 10, and each angle is 59 degrees. Then the supplement of each is 121 degrees.
What mistakes happen?
Using the rule when the lines are not parallel, which is invalid. Another is mixing corresponding angles with vertical angles, which are opposite each other at one intersection and are always equal. Remember that this property is a postulate, so it is accepted without proof in most courses.