如图,AB=AE,BC=ED,∠B=∠E,AF⊥CD于F.求证CF=DF.

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如图,AB=AE,BC=ED,∠B=∠E,AF⊥CD于F.求证CF=DF.
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如图,AB=AE,BC=ED,∠B=∠E,AF⊥CD于F.求证CF=DF.
如图,AB=AE,BC=ED,∠B=∠E,AF⊥CD于F.求证CF=DF.

如图,AB=AE,BC=ED,∠B=∠E,AF⊥CD于F.求证CF=DF.
连接AC和AD
∵AB=AE
BC=DE
∠B=∠E
∴△ABC≌△AED(SAS)
∴AC=AD
∵AF⊥CD即△ACF和△ADF是直角三角形
AF=AF
AC=AD
∴RT△ACF≌△ADF(HL)
∴CF=DF