# In triangles ABC and A1B1C1 BD and B1D1 are medians, angle A

October 3, 2021 | education

| **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.