Since triangles ABC and A1B1C1 are equal, then AB = A1B1, BC = B1C1, AC = A1C1, angle A = A1, angle B = B1, angle C = C1.
BH and B1H1 heights, then triangles ABH and A1B1C1 are rectangular in which the angle A1 = A, AB = A1B1, then the triangles are equal in acute angle and hypotenuse, and then BH = B1H1.
ВН and В1Н1 are bisectors, then in triangles ВСМ and В1С1М1 the angle CBM = С1В1М1, angle С = С1, side ВС = В1С1, then triangles ВСМ and В1С1М1 are equal in side and two adjacent angles, and then ВМ = В1М1, which was required to prove.
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