如图,六边形ABCDEF中,AB//DE,BC//EF,CD//AF,对边之差BC-EF=ED-AB=AF-CD>0,求证:该六边形的各角相等.
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![如图,六边形ABCDEF中,AB//DE,BC//EF,CD//AF,对边之差BC-EF=ED-AB=AF-CD>0,求证:该六边形的各角相等.](/uploads/image/z/14587858-10-8.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%85%AD%E8%BE%B9%E5%BD%A2ABCDEF%E4%B8%AD%2CAB%2F%2FDE%2CBC%2F%2FEF%2CCD%2F%2FAF%2C%E5%AF%B9%E8%BE%B9%E4%B9%8B%E5%B7%AEBC%EF%BC%8DEF%EF%BC%9DED%EF%BC%8DAB%EF%BC%9DAF%EF%BC%8DCD%EF%BC%9E0%2C%E6%B1%82%E8%AF%81%EF%BC%9A%E8%AF%A5%E5%85%AD%E8%BE%B9%E5%BD%A2%E7%9A%84%E5%90%84%E8%A7%92%E7%9B%B8%E7%AD%89.)
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如图,六边形ABCDEF中,AB//DE,BC//EF,CD//AF,对边之差BC-EF=ED-AB=AF-CD>0,求证:该六边形的各角相等.
如图,六边形ABCDEF中,AB//DE,BC//EF,CD//AF,对边之差BC-EF=ED-AB=AF-CD>0,求证:该六边形的各角相等.
如图,六边形ABCDEF中,AB//DE,BC//EF,CD//AF,对边之差BC-EF=ED-AB=AF-CD>0,求证:该六边形的各角相等.
参考
∠F=120°;将FA平移至EG,和将BA平移至CH,CH延长交EG于I(如图);
则GH=AH-AG=BC-FE,
GI=EG-CD=AF-CD
HI=CI-CH=DE-AB
由已知BC-EF=ED-AB=AF-CD>0
所以GH=GI=HI,△GHI是等边三角形
所以∠IGH=60°,∠F=∠AGE=180°-∠IGH=120°