SOLUTION: Hello, I want to know, Does the median from the vertex of 90 degree angle to the hypotenuse bisects the "Angle" in equal parts? Or it is only in the case of isosceles triangle?

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Question 841430: Hello,
I want to know, Does the median from the vertex of 90 degree angle to the hypotenuse bisects the "Angle" in equal parts?
Or it is only in the case of isosceles triangle?
And I would like to know more about the properties of median and altitude of a right angle triangle.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
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).