A Lemma of Equal Areas

Let $A, B, C$ be three collinear points. $D, E$ are two points on one side with respect to line that contains $A, B, C$ and such that $AD∥BE$ and $BD∥CE$. $M$ is midpoint of $AC$. Then

 $(DEM)=\dfrac{(ABD)+(BCE)}{2}$.

Read more »