# Median of a Triangle

• Dec 22nd 2009, 07:20 AM
sologuitar
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.
• Dec 22nd 2009, 08:03 AM
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 $x+y=90^o$.