△ABC的三边abc满足a²+b²+c²=ab+bc+ac,试判断△ABC的形状

△ABC的三边abc满足a²+b²+c²=ab+bc+ac,试判断△ABC的形状
△ABC的三边abc满足a²+b²+c²=ab+bc+ac,试判断△ABC的形状

△ABC的三边abc满足a²+b²+c²=ab+bc+ac,试判断△ABC的形状
a²+b²+c²=ab+bc+ac
2a²+2b²+2c²=2ab+2bc+2ac
(a-b)²+(b-c)²+(a-c)²=0
a-b=0,b-c=0,a-c=0
∴a=b=c
∴△ABC是等边三角形