如圖，菱形ABCD的對角線AC，BD相交於O點，E，F分別是AB，BC邊上的中點，連接EF．若EF=，BD=4...

問題詳情：

如圖，菱形ABCD的對角線AC，BD相交於O點，E，F分別是AB，BC邊上的中點，連接EF．若EF=，BD=4，則菱形ABCD的周長為（　　）                                                                         

A．4                            B．4                       C．4                       D．28

【回答】

C【考點】菱形的*質；三角形中位線定理．                                          

【分析】首先利用三角形的中位線定理得出AC，進一步利用菱形的*質和勾股定理求得邊長，得出周長即可．                                               

【解答】解：∵E，F分別是AB，BC邊上的中點，EF=，                          

∴AC=2EF=2，                                                                              

∵四邊形ABCD是菱形，                                                                         

∴AC⊥BD，OA=AC=，OB=BD=2，                                               

∴AB==，                                                                        

∴菱形ABCD的周長為4．                                                                 

故選：C．                                                                                         

【點評】此題考查菱形的*質，三角形的中位線定理，勾股定理，掌握菱形的*質是解決問題的關鍵．                 

知識點：特殊的平行四邊形

題型：選擇題