VTMO 2026 - Grade 8 - Final - SET 4 - Self-study Question 3

In quadrilateral $ABCD$, let $M,N$ be the midpoints of $BC,AD$, respectively. Let $P=AM\cap BN$ and $Q=DM\cap CN$. Prove that $S_{PAB}+S_{QCD}=S_{MPNQ}$, where $S$ denotes area.