VTMO 2026 - Grade 8 - Final - SET 6 - Self-study Question 5

In parallelogram $ABCD$, take points $E,F$ on side $AB$, with $E$ between $A$ and $F$. Let $M=DE\cap CF$, and use $S$ to denote area.

a) Prove $S_{ADM}+S_{BCM}=S_{DFC}$.

b) Prove $S_{MAB}=S_{MDF}$.