Points $M$ and $N$ are the midpoints of sides $AB$ and $CD$, respectively of quadrilateral $ABCD$. It is known that $BC // AD$ and $AN = CM$. Is it true that $ABCD$ is parallelogram?
Problem
Source: 2017 Oral Moscow Geometry Olympiad grades 8-9 p3
Tags: geometry, parallelogram, midpoints