Question 841430
The median emanating from the 90 deg angle bisects the right angle only when the triangle is a right isosceles triangle.


Let ABC be the right triangle with right angle A, and let M be the midpoint of BC. It can be shown that BM = CM = AM, as M is the circumcenter. Triangles BMA and CMA are isosceles, so if angle MAB = angle MAC = 45 deg, this implies angle B = angle C = 45 deg (right isosceles triangle).