如图,AB∥DE,AC∥DF,BE=CF.求证:△ABC≌△DEF.
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如图,AB∥DE,AC∥DF,BE=CF.求证:△ABC≌△DEF.
![](http://img.wesiedu.com/upload/9/f1/9f140d3193e83022b74fe39dad685ec0.jpg)
![](http://img.wesiedu.com/upload/9/f1/9f140d3193e83022b74fe39dad685ec0.jpg)
![如图,AB∥DE,AC∥DF,BE=CF.求证:△ABC≌△DEF.](/uploads/image/z/2317677-69-7.jpg?t=%E5%A6%82%E5%9B%BE%EF%BC%8CAB%E2%88%A5DE%EF%BC%8CAC%E2%88%A5DF%EF%BC%8CBE%3DCF%EF%BC%8E%E6%B1%82%E8%AF%81%EF%BC%9A%E2%96%B3ABC%E2%89%8C%E2%96%B3DEF%EF%BC%8E)
证明:∵AB∥DE,AC∥DF,
∴∠B=∠DEF,∠F=∠ACB.
∵BE=CF,
∴BE+CE=CF+EC.
∴BC=EF.
∴△ABC≌△DEF (ASA).
∴∠B=∠DEF,∠F=∠ACB.
∵BE=CF,
∴BE+CE=CF+EC.
∴BC=EF.
∴△ABC≌△DEF (ASA).
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