Lets construct a transversal to see how they interact with parallel lines. These are matched in measure and position with a counterpart. Usually we work with transversals when they cross parallel lines, like the two tracks of a railroad. So the converse of the parallel lines there is true. A Line Crosses A Pair of Parallel Lines If a set of 2 parallel lines, line l and line m, are crossed or cut by another line, line n, we say 'a set of parallel lines are cut by a transversal.' Each of the parallel lines cut by the transversal has 4 angles surrounding the intersection. If you have one pair of corresponding angles that are congruent you can say these two lines must be parallel. That's enough to say that they're parallel.ДЄnd finally, corresponding angles. That is these two angles right here that are alternate exterior, if those two are congruent, you don't even need to know about these interior ones. If two lines and a transversal form alternate interior angles, notice I abbreviated it, so if these alternate interior angles are congruent, that is enough to say that these two lines must be parallel. So the question is, if we have two lines that might be parallel and they're intersected by a transversal, can we do the converse of the parallel lines theorem? Which says, if we have alternate interior angles or alternate exterior angles, or corresponding angles that are congruent, is that enough to say that these two lines are parallel? And as we read right here, yes it is.

Parallel lines cut by a transversal