Let $ABCD$ be a quadrilateral. Prove that if $\overline{AB}$ is congruent to $\overline{CD}$, and $\angle BCD$ is congruent to $\angle DAB$, then $ABCD$ is a parallelogram.
I am feeling stuck because I can't find any avenue to go unless I can somehow prove an angle bisector exists between a diagonal and the pair of congruent angles.