Equal segments AK, BL, CM are plotted on the sides of an equilateral triangle ABC. Prove that triangle KLM is equilateral.

Triangles AKM, CML and BKL are equal, since the angles in an equilateral triangle are equal, AK = BL = CM; AM = CL = BK;
Hence KL = KM = LM, that is, the triangle KLM is equilateral;

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