Question

初二数学题 辅助线已做 有图

若三角形abc为等腰直角三角形 角man=135度 求BM^2+CN^2/MN^2的值是否变 做ck=cn并垂直x轴

Answer 1

因为三角形ABC为等腰直角三角形，所以角ABM=角ACN；
连接KN，已知CK=CN且垂直X轴，可知三角形KCN为等腰直角三角形；
又因为三角形ABC为等腰直角三角形，则角ABN=角ACM=135度=角MAN，AB=AC,可知三角形ABN全等于三角形ACM，且为等腰三角形；
所以AN=AM，所以三角形MAN类似于三角形ABN和三角形ACM。
所以CM=BN=AB=AC；则：BC+CM=NB+BC=AB+BC=AC+BC=CN=BM；
则MN=2AB+BC=2AC+BC,所以BM^2+CN^2/MN^2的值不变。

看懂了就看，看不懂随意。

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瞎搞

追答

你那^2是乘还是平方？

Answer 2

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Answer 3

请问是【BM*2+CN*2】/MN*2吗

追问

是啊 证明2个三角形全等可是我不会了啊55