Points M and N are marked at the base of the isosceles triangle ACB so that BM = CN.

Points M and N are marked at the base of the isosceles triangle ACB so that BM = CN. Prove that triangle BAM is equal to triangle CAN.

Since, by condition, triangle ABC is isosceles, its angles at the base of BC are equal.

Angle ABC = AСB, then angle ABM = AСН.

By condition, BM = CH, and AB = AC as the lateral sides of an isosceles triangle.

Then in the triangles BAC and СAН AB = AC, BM = CH, the angle ABM = AСН, which means that the triangles BAM and СAН are equal on two sides and yeah between them, the first sign of the equality of triangles, which was required to be proved.