Opposite Sides Equal implies Parallelogram

Theorem
Let $ABCD$ be a convex quadrilateral with $AB = CD$ and $BC = AD$.

Then $ABCD$ is a parallelogram.

Proof
Join $AC$.

From (7) and (8), $ABCD$ is a parallelogram by definition from $\left({7}\right)$ and $\left({8}\right)$.