IGO 2022 E2

An isosceles trapezoid $ABCD$ $(AB \parallel CD)$ is given. Points $E$ and $F$ lie on the sides $BC$ and $AD$ , and the points $M$ and $N$ lie on the segment $EF$ such that $DF = BE$ and $FM = NE$ . Let $K$ and $L$ be the foot of perpendicular lines from $M$ and $N$ to $AB$ and $CD$ , respectively. Prove that $EKFL$ is a parallelogram.

Proposed by Mahdi Etesamifard