Question 2
In trapezoid $ABCD$, $AB\parallel CD$ and $AB\lt CD$. The lines $DA$ and $CB$ extended meet at $I$. Let $E$ be a point on $CD$, and let $IE$ meet $AB$ at $F$. Take any point $P$ on the ray opposite to ray $BD$. The line $PF$ meets $AD$ at $M$, and $PE$ meets $BC$ at $N$. Prove that $MN\parallel AB$.
