+433 In parallelogram EFGH, let M be the point on \overline{EF} such that FM:ME = 1:1, and let N be the point on \overline{EH} such that HN:NE = 1:1. Line segments \overline{FH} and \overline{GM} intersect at P, and line segments \overline{FH} and GN intersect at Q. Find PQ/FH.
+130071 
Triangle HQN similar to triangle FQG Triangle MPF similar to triangle GPH
HQ / HN = FQ / FG MF / PF = GH / PH
HQ / 1 = FQ / 2 1 / PF = 2 / PH
HQ/FQ = 1/2 PF / PH= 1/2
HQ = (1/3)FH
PF = ( 1/3)FH
PQ = FH - PF - HQ = FH - (1/3)FH - (1/3)FH = (1/3)FH
PQ / FH = (1/3)FH / FH = 1/3
