Medians drawn to the equal sides of the isosceles triangle are equal in length. Yes. We shall prove it.
Let ABC be an isosceles triangle with AB=AC, the given condition.
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.
To prove that BE=CE.
Consider the 2 triangles ABE and ACD:
AB=AC, given that in triangle ABC , AB = AC.
AD=AE, as D and E are mid points of AB and AC, the equal sides of triangle ABC.
A is the common angle to both triangles ABE and ACD.
Thererefore, side, inclided angle, side of one triangle is respectively equal to those of the other triangle.Hence the triangles considered are congruent to each other. So, the side AE of ABE is equal to side CD of the triangle ACD. That completes our proof.