Median of Trapezoid is Parallel to Bases

Theorem
Let $\Box ABCD$ be a trapezoid such that $AB$ and $DC$ are the bases.


 * Median-of-Trapezoid.png

Let $E$ be the midpoint of $AD$.

Let $F$ lie on $BC$.

Then:
 * $EF$ is parallel to both $AB$ and $DC$


 * $F$ is the midpoint of $BC$.
 * $F$ is the midpoint of $BC$.

That is, the median of $\Box ABCD$ is parallel to the bases of $\Box ABCD$.