Question

If two medians of a triangle are equal, prove that the triangle formed by a segment of each median and the third side is an isosceles triangle.

Answer 1

Let the triangle be ABC, and where the medians AD and BE intersect be M.

The three medians intersect at the centroid, and divide each other in the ratio 1:2

That means that AM = BM and the triangle ABM is isosceles.

Answer 2

bn