Prove that the midpoints of the sides of an equilateral triangle are also the vertices of an equilateral triangle.

univerkov | February 13, 2021 | education

Consider a triangle A1B1C1 obtained from the midpoints of the sides AB; Sun; AC. AA1 = A1B; BB1 = B1C; CC1 – C1 A.
A1B1 = 1/2 * AB = B1C1 = 1/2 * AB = A1C1 = 1/2 * BC, as halves of equal sides of triangle ABC, and it turns out that triangle A1B1C1 is also equilateral.

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