In triangles ABC and A1B1C1 BD and B1D1 are medians, angle A = Angle A1, angle BDA = angle B1D1A1. Prove that triangle BDC is similar to B1D1C1.
Since triangles ABC and A1B1C1 are similar, the ratios of their similar sides and dimensions are equal to the coefficient of similarity.
AC / A1C1 = K.
Since BD and B1D1 are medians, then CD / C1D1 = K.
The medians of similar triangles drawn to the similar side are also similar. BD / B1D1 = K.
The angle ВDА = В1D1А1, then the adjacent angles ВСD = В1D1С1.
Then the triangles ВDC and В1D1С1 are similar in two proportional sides and the angle between them, which was required to be proved.
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