Question

Prove that the medians corresponding to equal sides of an isosceles triangle are equal.

Answer 1

Let ABC be an isosceles triangle with AB = AC.
Let D and E be the mid points of AB and AC.
Join BE and CD.
Then BE and CD are the medians of this isosceles triangle.
In ΔABE and ΔACD
AB = AC   ...(given)
AD = AE  ...(D and E are mid points of AB and AC)
∠A = ∠A  ...(common angle)
Therefore, ΔABE ≅ ΔACD  ...(SAS criteria)
Hence, BE = CD.