If a, B and C are the three sides of a triangle, and a & # 178; + B & # 178; + C & # 178; = AB + BC + Ca, try to judge the shape of the triangle and explain the reason

If a, B and C are the three sides of a triangle, and a & # 178; + B & # 178; + C & # 178; = AB + BC + Ca, try to judge the shape of the triangle and explain the reason

a²+b²+c²=ab+bc+ca
2a²+2b²+2c²=2ab+2bc+2ca
2a²+2b²+2c²-2ab-2bc-2ca=0
(a²-2ab+b²)+(b²-2bc+c²)+(a²-2ac+c²)=0
(a-b)²+(b-c)²+(a-c)²=0
∴a-b=0,b-c=0,a-c=0
∴a=b=c
The triangle is equilateral

Elden Ring Premiere

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