．如圖，在矩形ABCD中，AB=4，AD=6，E是AB邊的中點，F是線段BC上的動點，將△EBF沿EF所在直線...

問題詳情：

．如圖，在矩形ABCD中，AB=4，AD=6，E是AB邊的中點，F是線段BC上的動點，將△EBF沿EF所在直線摺疊得到△EB′F，連接B′D，則B′D的最小值是（　　）                                              

A．2﹣2                B．6                            C．2﹣2                D．4

【回答】

A【考點】翻折變換（摺疊問題）．                                                        

【專題】壓軸題．                                                                              

【分析】當∠BFE=∠B'FE，點B′在DE上時，此時B′D的值最小，根據勾股定理求出DE，根據摺疊的*質可知B′E=BE=2，DE﹣B′E即為所求．                                                                           

【解答】解：如圖，當∠BFE=∠B'FE，點B′在DE上時，此時B′D的值最小，              

根據摺疊的*質，△EBF≌△EB′F，                                                        

∴EB′⊥B′F，                                                                                      

∴EB′=EB，                                                                                        

∵E是AB邊的中點，AB=4，                                                                   

∴AE=EB′=2，                                                                                    

∵AD=6，                                                                                          

∴DE==2，                                                                         

∴DB′=2﹣2．                                                                             

故選：A．                                                                                         

【點評】本題主要考查了摺疊的*質、全等三角形的判定與*質、兩點之間線段最短的綜合運用，確定點B′在何位置時，B′D的值最小，是解決問題的關鍵．                                                        

知識點：軸對稱

題型：選擇題