## Geometry: Common Core (15th Edition)

We have congruent vertical angles and congruent alternate interior angles, meaning that all corresponding angles in both triangles are congruent; therefore, by the AA Similarity Postulate, $\triangle RTO$ ~ $\triangle FTL$.
We are given a set of parallel lines that are cut by two transversals, $\overline{RF}$ and $\overline{OL}$. We know that in this case, alternate interior angles are congruent. So, we have at least one set of alternate interior angles in the two triangles. We can also see that $\angle RTO$ and $\angle FTL$ are vertical angles; therefore, they are congruent to one another. We have congruent vertical angles and congruent alternate interior angles, meaning that all corresponding angles in both triangles are congruent; therefore, by the AA Similarity Postulate, $\triangle RTO$ ~ $\triangle FTL$.