Question 573999: write a corrdinate proof to show that the three segments joining the midpoints of the sides of an isosceles triangle form another isosceles triangle
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Without loss of generality, suppose the coordinates of the triangle are (0,0), (1,0), and (1/2,a) where a is a real number. If you take the midpoint of each pair of points, you should obtain (1/2,0), (1/4, a/2), and (3/4, a/2) as the vertices of the new triangle. It is easy to check that the distance between (1/4, a/2) and (1/2,0) is the same as the distance between (3/4, a/2) and (1/2,0) (either by Pythagorean theorem or symmetry).
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