The median segment divides the triangle into 2 isosceles triangles and everything else is trivial.|ad|=|bc|2=|bd|soδadb is isosceles with∠dab=∠dbasimilarlyδadc is isosceles with ∠dac=∠dca∠cab=∠cad+∠bad=∠acb+∠abctherefore∠cab is a right angleandbc is the hypotenuse of a right-angled triangle.hope this