ABC and A1B1C1 are isosceles triangles with bases Ac and A1C1, points M and M1 are midpoints of BC and B1C1
| September 14, 2021 | education
ABC and A1B1C1 are isosceles triangles with bases Ac and A1C1, points M and M1 are midpoints of BC and B1C1, respectively. AB = A1B1, Am = A1M1. Prove that triangles ABC = A1B1C1.
1) Considering triangles ABM and A1B1M1, in which are equal: AB = A1B1; AM = A1M1; VM = B1M1, since VM = (1/2) * BC = B1M1 = (1/2) * B1C1. And BC = B1C1, so BC = AB = A1B1 = B1C1, as the sides of such a triangle.
2) In equal triangles ABM and A1B1M1 against equal sides AM = A1M1 there are equal angles <ABM = <A1B1M1.
3) Considering triangles ABC and A1B1C1, in which AB = A1B1; BC = B1C1, as a consequence of the equality of the sides, <ABC = <A1B1C1, as proved in paragraph 2).
They proved the equality of triangles ABC and A1B1C1.
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