Line Parallel to Base of Trapezoid which Bisects Leg also Bisects Other Leg

Theorem
Let $ABCD$ be a trapezoid whose bases are $AB$ and $CD$.

Let $EF$ be a straight line parallel to $AB$ and $CD$ which intersects its legs $AD$ and $BC$.

Let $EF$ bisect $AD$.

Then $EF$ also bisects $BC$.

Proof

 * Midline of Trapezoid.png