KöMaL 2021 C1668

The midpoints of sides $AB$, $BC$, $CD$, $DA$ of a parallelogram $ABCD$ are $E$, $F$, $G$, $H$, respectively. The lines $AF$ and $AG$ intersect diagonal $BD$ at points $K$ and $L$, respectively. Show that the sum of the areas of triangles $EFK$ and $GHL$ equals the area of triangle $EKL$.