如图,AB∥CD,AB∥CD,BE=CF,求证AF∥ED.
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如图,AB∥CD,AB∥CD,BE=CF,求证AF∥ED.
![](http://img.wesiedu.com/upload/0/ff/0fff7125383f35fa5795445257a1fc47.jpg)
![](http://img.wesiedu.com/upload/0/ff/0fff7125383f35fa5795445257a1fc47.jpg)
![如图,AB∥CD,AB∥CD,BE=CF,求证AF∥ED.](/uploads/image/z/17043440-32-0.jpg?t=%E5%A6%82%E5%9B%BE%2CAB%E2%88%A5CD%2CAB%E2%88%A5CD%2CBE%3DCF%2C%E6%B1%82%E8%AF%81AF%E2%88%A5ED.)
证明:∵AF=DE,
∴AF-EF=DE-EF,
即 AE=DF,
∵AB∥CD,
∴∠A=∠D,
在△ABE和△DCF中,
AB=CD
∠A=∠D
AE=DF
∴△ABE≌△DCF,
∴BE=CF.
∴AF-EF=DE-EF,
即 AE=DF,
∵AB∥CD,
∴∠A=∠D,
在△ABE和△DCF中,
AB=CD
∠A=∠D
AE=DF
∴△ABE≌△DCF,
∴BE=CF.
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