平行四边形ABCD,延长AD至E,使AD=DE,延长AB至F,使AB=BF,EM垂直AM,FN垂直AN,角AEM=角AFN,求证CN=CM

问题描述:

平行四边形ABCD,延长AD至E,使AD=DE,延长AB至F,使AB=BF,EM垂直AM,FN垂直AN,角AEM=角AFN,求证CN=CM

证明:连接BN,DM
BN=1/2AF=AB=CD
DM=1/2AE=AD=BC
角FBN=2角FAN=2角EAM=角EDM
=>角CBN=角CBF-角NBF=角CDE-角NBF=角CDE-角EDM=角CDM
=>三角形CBN全等于三角形MDC=>CN=CM
证毕!