Let $ABCD$ be a parallelogram, $E$ a point on the line $AB$, beyond $B, F$ a point on the line $AD$, beyond $D$, and $K$ the point of intersection of the lines $ED$ and $BF$. Prove that quadrilaterals $ABKD$ and $CEKF$ have the same area.
Problem
Source: VIII - Mathematics Regional Olympiad of Mexico Northeast 2008 P1
Tags: geometry, areas, parallelogram