KöMaL 2008 B4128

$P$ and $Q$ are two different points on the diagonal $AC$ of a parallelogram ABCD . The line through $P$ parallel to $AB$ intersects the sides $BC$ and $AD$ at $K$ and $L$, and the line through $Q$ parallel to $BC$ intersects the sides $AB$ and $CD$ at $M$ and $N$. Show that the areas of the triangles PNM and QKL are equal.