已知B(-2,0),C(2,0),点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在(2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.
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![已知B(-2,0),C(2,0),点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在(2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.](/uploads/image/z/12392120-56-0.jpg?t=%E5%B7%B2%E7%9F%A5B%EF%BC%88-2%2C0%EF%BC%89%2CC%EF%BC%882%2C0%EF%BC%89%2C%E7%82%B9A%E6%98%AFY%E8%BD%B4%E6%AD%A3%E5%8D%8A%E8%BD%B4%E4%B8%8A%E4%B8%80%E7%82%B9%2CCD%E2%8A%A5AC%E4%BA%A4Y%E8%BD%B4%E4%BA%8ED%2CM%E4%B8%BAAC%E4%B8%8A%E4%B8%80%E5%8A%A8%E7%82%B9%2CN%E4%B8%BAAB%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%B8%80%E5%8A%A8%E7%82%B9%2C%E4%B8%94%E6%BB%A1%E8%B6%B3AM%2BAN%3D2AC%2CMN%E4%BA%A4BC%E4%BA%8EE%2C%E8%BF%9EDE.%283%29%E5%9C%A8%EF%BC%882%29%E7%9A%84%E6%9D%A1%E4%BB%B6%E4%B8%8B%E9%97%AEBC%E5%88%86%E4%B9%8BEK%E7%9A%84%E5%80%BC%E6%98%AF%E5%90%A6%E5%8F%91%E7%94%9F%E5%8F%98%E5%8C%96%2C%E8%8B%A5%E4%B8%8D%E5%8F%98%2C%E6%B1%82%E5%85%B6%E5%80%BC.)
已知B(-2,0),C(2,0),点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在(2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.
已知B(-2,0),C(2,0),点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在(2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.
已知B(-2,0),C(2,0),点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在(2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.
(1)作辅助线,连接DM,BD,过点N作NL 垂直于AC,交x轴点L
则有:AB=AC,BD=BC,BD垂直于AB
又AM+AN=2AC,AN=AB+ BN
BN=MC
在三角形MKC和NLB中,BN=MC,角LBN
=ABC=MCK
两三角形全等,MK=NL
在三角形NEL和MEK中,MK=NL,对角相等,两个三角形全等,ME=NE
在直角三角形DCM和DBN中,BD=BC,BN=MC
两个三角形全等
DM=DN
则:E为等腰三角形DMN中线,故:DE垂直MN
证明:过N做NF⊥x轴于F
∵NF⊥x轴 MK⊥BC
∴∠NFC=∠MKF=90°
∵AB=AC
∴∠ABC=∠MCK
∵∠NBF=∠ABC
∴∠NBF=∠MCK
在△BFN和△MCK中
∠NFC=∠MKF=90°
∠FBN=∠MCK
BN=CM
∴△BFN≌△M...
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证明:过N做NF⊥x轴于F
∵NF⊥x轴 MK⊥BC
∴∠NFC=∠MKF=90°
∵AB=AC
∴∠ABC=∠MCK
∵∠NBF=∠ABC
∴∠NBF=∠MCK
在△BFN和△MCK中
∠NFC=∠MKF=90°
∠FBN=∠MCK
BN=CM
∴△BFN≌△MCK(AAS)
∴NF=MK
在△EFN和△MEK中
∠BEN=∠MEK
∠NFC=∠MKF
NF=MK
∴△EFN≌△MEK(AAS)
∴EN=ME
连接BD,MD,DN
∵CD⊥AC
∴∠DCA=90°
∵BD⊥AN
∴∠DBN=90°
在△BND和△MCD中
BN=CM
∠NBD=∠MCD=90°
BD=CD
∴△BND≌△MCD(SAS)
∴DN=DM
∵NE=ME
∴DE⊥MN
∵△ENF≌△MEK
∴EF=EK
∵△BFN≌△MKC
∴BF=CK
∴EK=EF=1/2FK
=1/2(BF+OB+OC-CK)
=1/2(OB+OC)
∴EK/BC=1/2
收起
证明:过N做NF⊥x轴于F
∵NF⊥x轴 MK⊥BC
∴∠NFC=∠MKF=90°
∵AB=AC
∴∠ABC=∠MCK
∵∠NBF=∠ABC
∴∠NBF=∠MCK
在△BFN和△MCK中
∠NFC=∠MKF=90°
∠FBN=∠MCK
BN=CM
∴△BFN≌△MCK(AAS)
∴NF=MK
在...
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证明:过N做NF⊥x轴于F
∵NF⊥x轴 MK⊥BC
∴∠NFC=∠MKF=90°
∵AB=AC
∴∠ABC=∠MCK
∵∠NBF=∠ABC
∴∠NBF=∠MCK
在△BFN和△MCK中
∠NFC=∠MKF=90°
∠FBN=∠MCK
BN=CM
∴△BFN≌△MCK(AAS)
∴NF=MK
在△EFN和△MEK中
∠BEN=∠MEK
∠NFC=∠MKF
NF=MK
∴△EFN≌△MEK(AAS)
∴EN=ME
连接BD,MD,DN
∵CD⊥AC
∴∠DCA=90°
∵BD⊥AN
∴∠DBN=90°
在△BND和△MCD中
BN=CM
∠NBD=∠MCD=90°
BD=CD
∴△BND≌△MCD(SAS)
∴DN=DM
∵NE=ME
∴DE⊥MN
∵△ENF≌△MEK
∴EF=EK
∵△BFN≌△MKC
∴BF=CK
∴EK=EF=1/2FK
=1/2(BF+OB+OC-CK)
=1/2(OB+OC)
∴EK/BC=1/2
收起
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