In this question, We have to prove that:

The median and altitude of an isosceles triangle are same

The diagram for the given question is as follows:

This can be proved as follows:

First of all we have to draw a line segment AD which is perpendicular to BC. This is an altitude for this triangle

Now,

From the figure it can also be observed that the length of BD and DC is also same

Therefore,

AD is also median of this isosceles triangle

Hence, proved