The three sides a, B and C of △ ABC satisfy that the square of a + the square of B + the square of C = AB + BC + ca

The three sides a, B and C of △ ABC satisfy that the square of a + the square of B + the square of C = AB + BC + ca

A ^ 2 + B ^ 2 + C ^ 2 = AB + BC + Ca 2A ^ 2 + 2B ^ 2 + C ^ 2 = 2Ab + 2BC + 2ca 2A ^ 2 + 2B ^ 2 + C ^ 2-2ab-2bc-2ca = 0 (a-b) ^ 2 + (B-C) ^ 2 + (C-A) ^ 2 = 0 (a-b) ^ 2 > = 0, (B-C) ^ 2 > = 0, (C-A) ^ 2 > = 0. Therefore, a = b = C this triangle is equilateral

How to restore the regular triangle figure in the plane visual graph?

If there is no mistake, the object should be a regular triangular prism
But you have to be high to restore