已知:如图,AB=DC,AE=BF,CE=DF,∠A=60°.
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已知:如图,AB=DC,AE=BF,CE=DF,∠A=60°.
![](http://img.wesiedu.com/upload/5/81/5814b014351766a88e65ab8b76a44711.jpg)
(1)求∠FBD的度数.
(2)求证:AE∥BF.
![](http://img.wesiedu.com/upload/5/81/5814b014351766a88e65ab8b76a44711.jpg)
(1)求∠FBD的度数.
(2)求证:AE∥BF.
![已知:如图,AB=DC,AE=BF,CE=DF,∠A=60°.](/uploads/image/z/18993077-53-7.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E5%A6%82%E5%9B%BE%EF%BC%8CAB%3DDC%EF%BC%8CAE%3DBF%EF%BC%8CCE%3DDF%EF%BC%8C%E2%88%A0A%3D60%C2%B0%EF%BC%8E)
(1)∵AB=CD,
∴AB+BC=CD+BC,
∴AC=BD,
在△AEC和△BFD中
AE=BF
AC=BD
CE=DF
∵△AEC≌△BFD,
∴∠A=∠FBD,
∴∠A=∠FBD,
∵∠A=60°,
∴∠FBD=60°;
(2)证明:∵∠A=∠FBD,
∴AE∥BF.
∴AB+BC=CD+BC,
∴AC=BD,
在△AEC和△BFD中
AE=BF
AC=BD
CE=DF
∵△AEC≌△BFD,
∴∠A=∠FBD,
∴∠A=∠FBD,
∵∠A=60°,
∴∠FBD=60°;
(2)证明:∵∠A=∠FBD,
∴AE∥BF.
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