If a, B and C are the lengths of the three sides of a triangle, and A2 + B2 + C2 = AB + BC + Ca, we can judge the shape of the triangle and explain the reason

If a, B and C are the lengths of the three sides of a triangle, and A2 + B2 + C2 = AB + BC + Ca, we can judge the shape of the triangle and explain the reason

A triangle is an equilateral triangle. A ^ 2 + B ^ 2 + C ^ 2 = AB + BC + ca2a ^ 2 + 2B ^ 2 + 2C ^ 2-2ab-2bc-2ca = 0A ^ 2-2ab + B ^ 2 + B ^ 2-2bc + C ^ 2 + C ^ 2-2ca + A ^ 2 = 0 (a-b) ^ 2 + (B-C) ^ 2 + (C-A) ^ 2 = 0a-b = 0 a = bb-c = 0 B = cc-a = 0 C = AA = b = C