In an acute triangle ABC, the feet of the perpendiculars from A and C to the opposite sides are D and E, respectively. The line passing through E and parallel to BC intersects AC at F, the line passing through D and parallel to AB intersects AC at G. The feet of the perpendiculars from F to DG and GE are K and L, respectively. KL intersects ED at M. Prove that FM⊥ED. geometry proposedperpendicular linesgeometry