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Math Help - Median of a Triangle

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    Median of a Triangle

    Show that if a median of a triangle is one-half the side to which it is drawn, then it must be right.
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    Hello sologuitar
    Quote Originally Posted by sologuitar View Post
    Show that if a median of a triangle is one-half the side to which it is drawn, then it must be right.
    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^o (can you see why?). Therefore x+y=90^o.

    Can you fill in the details now?

    Grandad
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