In an isosceles triangle ABC Points K and M are the midpoints of sides AB and BC, respectively.

In an isosceles triangle ABC Points K and M are the midpoints of sides AB and BC, respectively. BC is the median of a triangle. Prove that triangle AKD is equal to triangle CMD.

Most likely, the median of the triangle is BD.
Consider triangles AKD and CMD, in them:
AD = CD (BD is the conditional median).
AK = CM (points K and M are the midpoints of equal sides).
∠A = ∠C (triangle ABC – isosceles).
We have the first sign of equality of triangles.
The triangles are equal, as required.