△ABC的三边abc满足a²+b²+c²=ab+bc+ac,试判断△ABC的形状
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/29 09:12:30
![△ABC的三边abc满足a²+b²+c²=ab+bc+ac,试判断△ABC的形状](/uploads/image/z/3722437-37-7.jpg?t=%E2%96%B3ABC%E7%9A%84%E4%B8%89%E8%BE%B9abc%E6%BB%A1%E8%B6%B3a%26%23178%3B%2Bb%26%23178%3B%2Bc%26%23178%3B%3Dab%2Bbc%2Bac%2C%E8%AF%95%E5%88%A4%E6%96%AD%E2%96%B3ABC%E7%9A%84%E5%BD%A2%E7%8A%B6)
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△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