Problem #PRU-5107

Problem

Consider two congruent triangles $A B C$ and $A_{1} B_{1} C_{1}$ . We draw a point $M$ on the side $B C$ and a point $M_{1}$ on the side $B_{1} C_{1}$ such that the ratio of lengths $B M : M C$ is equal to the ratio of lengths $B_{1} M_{1} : M_{1} C_{1}$ . Prove that $A M = A_{1} M_{1}$ .

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