Show that a line is parallel to trapezoid bases

Question

$$ABCD:AB||CD, AB \neq CD, AD = BC$$ $M$ is the midpoint of $AB$, $P = MD \cap AC$, $Q =MC \cap BD$; Show that $PQ||AB$ using symmetry. I've tried to show that $PP_1 = QQ_1$ ($PP_1\bot AB, P_1 \in AB; QQ_1 \bot AB, Q_1 \in AB$) but I think it isn't working. I've tried to use $MN$ where $N$ is the midpoint of $DC$ but I still can't figure it out. I would be very grateful if you could help me.