+1533 I don't know what to do here!!!! Help!!!
In parallelogram $EFGH,$ let $M$ be the point on $\overline{EF}$ such that $FM:ME = 3:5,$ and let $N$ be the point on $\overline{EH}$ such that $HN:NE = 2:5.$ Line segments $\overline{FH}$ and $\overline{GM}$ intersect at $P,$ and line segments $\overline{FH}$ and $\overline{GN}$ intersect at $Q.$ Find $\frac{PQ}{FH}.$
+129849 
Triangle HQN similar to Triangle FQG
HN / FG = 2 / 7
Therefore HQ / FQ = 2 / 7
Therefore HQ / (HQ + FQ) = HQ / HF = 2 / ( 2 + 7) = 2/9 ⇒ HQ = (2/9) HF
Triangle PFM similar to Triangle PHG
FM / HG = 3 / 8
Therefore PF / PH = 3 / 8
Therfore PF / (PF + PH) = PF / HF = 3 /( 3 + 8) = 3 / 11 ⇒ PF = (3/11) HF
Getting a common denominator between 9 and 11
HQ = 22/99FH
PF = 27/99 FH
Therefore
FH - HQ - PF = PQ
FH - (22/99)FH - (27/99)FH = PQ
(50/99)FH = PQ
Therefore
PQ / FH = 50 / 99
