题目

如图，在四边形ABCD中，E是BC边的中点，连接DE并延长，交AB的延长线于F点，AB=BF．添加一个条件，使四边形ABCD是平行四边形．你认为下面四个条件中可选择的是（　　）                                                                                             A．AD=BC                   B．CD=BF                   C．∠A=∠C                D．∠F=∠CDE 答案：D【分析】把A、B、C、D四个选项分别作为添加条件进行验证，D为正确选项．添加D选项，即可证明△DEC≌△FEB，从而进一步证明DC=BF=AB，且DC∥AB．                                              【解答】解：添加：∠F=∠CDE，                                                           理由：                                                                                                ∵∠F=∠CDE，                                                                                  ∴CD∥AB，                                                                                       在△DEC与△FEB中，，                                                ∴△DEC≌△FEB（AAS），                                                                    ∴DC=BF，                                                                                         ∵AB=BF，                                                                                         ∴DC=AB，                                                                                         ∴四边形ABCD为平行四边形，                                                               故选：D．                                                                                          【点评】本题是一道探索性的试题，考查了平行四边形的判定，熟练掌握平行四边形的判定方法是解题的关键．                                               　

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