Question 251410: show that if a median of a triangle is one-half the side to which it is drawn, then it must be right
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! Do you know the theorem "The angle in a semicircle is a right-angle"? If you do, use this, noting that the three vertices of the triangle are equidistant from the mid-point of the side to which the median is drawn. Thus, this point is the centre of the circle passing through the vertices of the triangle - and using the above theorem, the result follows.
If you don't know this circle theorem, then use the fact that you have two isosceles triangles - one on either side of the median. Then look at the angles in these triangles that are equal. Call the size of one pair x , and the size of the other pair y . Then 2x + 2y = 180 (can you see why?).
Therefore x + y = 90 .
Can you fill in the details now?
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