KöMaL 2021 C1671

Line segments $AE$, $BF$, $CG$, $DH$ are perpendicular to the plane $S$ of parallelogram $ABCD$, in the same half space formed by plane $S$. $T$ and $t$ denote the areas of quadrilaterals $CGEA$ and $DHFB$, respectively. Prove that if $\frac{T}{t}=\frac{AC}{BD},$ then the points $E$, $F$, $G$, $H$ are coplanar.