Angle bisection by means of a perpendicular to the side of a

The applet illustrates the property by which the straight line issuing from E, the point of intersection of the diagonals of the trapezoid, and he is perpendicular to the side BC, bisects the angle IMJ (DJ=JC, AI=IB). When the vertices of the trapezoid A, B, C are dragged, the property is conserved. In any condition the points J, E, I, F remain on a straight line according to the Steiner's theorem.