KöMaL 2019 A755

Prove that every polygon that has a center of symmetry can be dissected into a square such that it is divided into finitely many polygonal pieces, and all the pieces can only be translated. (In other words, the original polygon can be divided into polygons $A_1, A_2,\dots, A_n$, a square can be divided into polygons a $B_1, B_2,\dots, B_n$ such that for $1\le i\le n$ polygon $B_i$ is a translated copy of polygon $A_i$.)