in the triangle FGH, FA is the altitude, with A belonging to GH, and AM is the median in the triangle FGH. In the half-plane opposite to the segment GH, F, a point is taken with E, so that EH is perpendicular to GH and GH=FA. Let HT be the median in triangle AHE. Show that AM=HT

how do we draw the triangle, how do we put the points on the sides?