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

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
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

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
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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请问是【BM*2+CN*2】/MN*2吗