已知AB=CD,AE=CF,BF=DE,说明:(1)BE=DF (2)BE//DF
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已知AB=CD,AE=CF,BF=DE,说明:(1)BE=DF (2)BE//DF
![](http://img.wesiedu.com/upload/b/ff/bff5a40ac11629849b6b545d99d6350d.jpg)
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![已知AB=CD,AE=CF,BF=DE,说明:(1)BE=DF (2)BE//DF](/uploads/image/z/17787917-29-7.jpg?t=%E5%B7%B2%E7%9F%A5AB%3DCD%2CAE%3DCF%2CBF%3DDE%2C%E8%AF%B4%E6%98%8E%3A%281%29BE%3DDF+%282%29BE%2F%2FDF)
证明:(1)∵AE=CF,AB=CD,AE=CF
∴△CDE≌△ABF
∴∠A=∠C
∴△CDF≌△ABE
∴BE=DF,∠ABE=∠CDF
(2)由上得知∠FBE=∠ABE+∠A=∠C+∠CDF=∠DFE
∴BE//DF
∴△CDE≌△ABF
∴∠A=∠C
∴△CDF≌△ABE
∴BE=DF,∠ABE=∠CDF
(2)由上得知∠FBE=∠ABE+∠A=∠C+∠CDF=∠DFE
∴BE//DF
如图,已知,AD=BC,AB=DC,DE=BF说明:(1)AE‖CF,(2)BE=DF
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