Let $ABCDE$ be a convex pentagon that has $AB < BC$, $AE <ED$ and $AB + CD + EA = BC + DE$. Variable points $F,G$ and $H$ are taken that move on the segments $BC$, $CD$ and $OF$ respectively . $B'$ is defined as the projection of $B$ on $AF$, $C'$ as the projection of $C$ on $FG$, $D'$ as the projection of $D$ on $GH$ and $E'$ as the projection of $E$ onto $HA$. Prove that there is at least one quadrilateral $B'C'D'E'$ when $F,G$ and $H$ move on their sides, which is a parallelogram.