如图,AB=AE,BC=ED,∠B=∠E,∠BAF=∠EAF,求证AF⊥CD

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如图,AB=AE,BC=ED,∠B=∠E,∠BAF=∠EAF,求证AF⊥CD

如图,AB=AE,BC=ED,∠B=∠E,∠BAF=∠EAF,求证AF⊥CD
如图,AB=AE,BC=ED,∠B=∠E,∠BAF=∠EAF,求证AF⊥CD

如图,AB=AE,BC=ED,∠B=∠E,∠BAF=∠EAF,求证AF⊥CD
连接AC,AD,在△ABC与△AED中,
∵AB=AE,BC=ED,∠B=∠E
∴△ABC≌△AED
∴AC=AD,∠BAC=∠EAD
又∵∠BAF=∠EAF
∴∠CAF=∠FAD
在△CAF与△FAD中
∵∠CAF=∠FAD
AC=AD AF=AF
∴△CAF≌△FAD
∴AF⊥CD