IGO 2021 E2

Points $K, L, M, N$ lie on the sides $AB, BC, CD, DA$ of a square $ABCD$ , respectively, such that the area of $KLMN$ is equal to one half of the area of $ABCD$ . Prove that some diagonal of $KLMN$ is parallel to some side of $ABCD$ .

Proposed by Josef Tkadlec - Czech Republic