In an isosceles triangle ABC, points K and M are the midpoints of the lateral sides AB and BC

In an isosceles triangle ABC, points K and M are the midpoints of the lateral sides AB and BC, respectively. BD is the median of the triangle. Prove that ΔВКD = ΔВМD.

Since the triangle is equilateral, the median BD is also the bisector of the angle ABC, and then the angle ABD = CBD.

In triangles BKD and BMD, side BD is common.

Points K and M are the midpoints of segments AB and BC, and since AB = BC, then BK = BM.

Then the triangles BKD and BMD are equal according to the first sign of equality of triangles – on two sides and the angle between them.

Q.E.D.