MathNet 2026 — Part 10 Question 154

Let $ABCD$ be a trapezoid with $AB \parallel CD$. Let $M$ and $N$ be the respective midpoints of $AB$ and $CD$. Diagonals $AC$ and $BD$ meet at $P$, and lines $AD$ and $BC$ meet at $Q$. Prove that $M$, $N$, $P$, and $Q$ are collinear.