Infographic Geometry Problem 919: Rhombus, Triangle, Perpendicular, 90 Degrees, Congruence. Level: High School, College, Mathematics Education

In a rhombus ABCD (figure below), P and F are on AB extended and G and Q are on AD extended, so that
angle APQ = angle AGF = 90 degrees. PQ meets CD and FG at N and E, respectively, FG meets BC at M. Prove that
FG + EN = EP + FM.