Prove that medians drawn from two vertices to equal sides of an isosceles triangle are equal.

Let OAB be an equilateral triangle with vertices (0, 0), (a, 0), and (a/2, a).

Let C and D be the mid-points of AB and OB respectively.

∴ C has coordinates (3a/4, a/2) and D has coordinates (a/4, a/2).

Length of OC = √[(3a/4)² + (a/2)²] = √[(9a²/16) + (a²/4)] = (a/4)√13

Length of AD = √[(a − a/4)² + (0 − a/2)²] = (a/4)√13

∴ Length of OC = Length of AD

Hence the proof.