在四边形ABCD中,AD//BC,∠ABC=∠DCB,AB=DC,AE=DF.

1、∵AD∥BC
∠ABC=∠DCB
∴∠DAB+∠ABC=∠ADC+∠DCB=180°
∴∠DAB=∠ADC
即∠FAB=∠EDC
∵AE=DF
∴AE+AD=AD+DF
即DE=AF
∵AB=CD
∴△ABF≌△CDE
∴F=CE
2、、∵AD∥BC
∠ABC=∠DCB
∴∠DAB+∠ABC=∠ADC+∠DCB=180°
∴∠DAB=∠ADC
∵AD=AD
AB=CD
∴△ABD≌△ACD
∴AC=BD
∴A和E、D和F重合
∴BF=CE
3、、∵AD∥BC
∠ABC=∠DCB
∴∠DAB+∠ABC=∠ADC+∠DCB=180°
∴∠DAB=∠ADC
即∠EAB=∠FDC
∵AE=DF
AB=CD
∴△ABE≌△CDF
∴BF=CE
4、、∵AD∥BC
∠ABC=∠DCB
∴∠DAB+∠ABC=∠ADC+∠DCB=180°
∴∠DAB=∠ADC
∴∠FAB=∠EDC
∵AE=DF
∴AE-AD=DF-AD
即AF=DE
∵AB=CD
∴△ABF≌△CDE
∴BF=CE