Answer
To simplify this process, we simply have to show that the triangle created by the second transversal is similar to the one created by the first transversal. If this is true, then the given statement will be true as well:
1. Each line is a transversal that intersects the parallel lines.
2. Thus, because corresponding angles are congruent, these two triangles have congruent base angles.
3. These two triangles also share an angle where the lines intersect. By the identity property, this angle is congruent to itself.
4. By AAA, this means that the two triangles are similar.
Since the two triangles are similar, this concludes our proof. After all, since similar triangles have constant proportions, this means that the lines will always intersect congruent segments on the transversal.
