IGO 2019 E2

As shown in the figure, there are two rectangles $ABCD$ and $PQRD$ with the same area, and with parallel corresponding edges. Let points $N,$ $M$ and $T$ be the midpoints of segments $QR,$ $PC$ and $AB$ , respectively. Prove that points $N,M$ and $T$ lie on the same line.

Proposed by Morteza Saghafian