Question 4
Trapezoid $ABCD$ has $AB \parallel CD , AB \lt CD$, and extensions $DA , CB$ meeting at I. $E$ lies on $CD , IE$ meets $AB$ at $F$. $P$ lies on the ray opposite $BD$. $PF$ meets $AD$ at $M$ and $PE$ meets $BC$ at $N$. Prove $MN \parallel AB$.