Category:Median of Trapezium is Parallel to Bases

This category contains pages concerning Median of Trapezium is Parallel to Bases:

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

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

Let $F$ lie on $BC$.

Then:

$EF$ is parallel to both $AB$ and $DC$

if and only if:

$F$ is the midpoint of $BC$.

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