I would like some help getting started with this problem. My initial thought was to try to get that $\angle BEC \cong \angle AED$. From there I could say that $\overline{EF}$ is the angle bisector. However, I could not find a way to show some kind of similarity.
Note: $ABCD$ is a trapezoid. Diagonals intersect at $P$. The line through $P$ parallel to the bases intersects $\overline{AB}$ and $\overline{CD}$ at points $E$ and $F$, respectively. Right angles at $B$ and $A$. Prove that $\overline{EF}$ is the angle bisector of $\angle CED$.
