The right triangle is in blue. Since it is a midpoint, clearly it is equidistant from the vertices that are opposite the 90 degree angle. Thus, we must prove that triangle AEB is isosceles. Since angle A and angle B are both bisected 90 degree angles, they have equal measures. Since the base angles are the same, it is isosceles. Thus, the midpoint of the hypotenuse is equidistant from the vertices.