Corresponding angles

The transversal makes two groups of four angles: one where it crosses l, one where it crosses m. Angles in the same position in each group are corresponding angles: 1 and 5, 2 and 6, 3 and 7, 4 and 8. (Trace a capital F: the two angles tucked under its arms are corresponding.)

Try it. Draw a line l and a transversal t crossing it at X. Say the angle there is 60°. Mark a point Y further along t, and through Y draw a line m that also makes 60° with t, in the same position (copy the angle with tracing paper or a protractor). What do l and m look like? Parallel!

We made the corresponding angles equal, and the lines came out parallel. So: if corresponding angles are equal, the lines are parallel.

It works the other way too. Take two lines that are parallel, trace one angle, and slide the tracing to its corresponding angle: it fits exactly. So: when two parallel lines are crossed by a transversal, corresponding angles are equal.

And try this: draw a transversal across two lines that are not parallel and make a pair of corresponding angles equal. You can't! If the lines aren't parallel, corresponding angles are never equal.