题目

若顺次连结四边形各边中点所得的四边形是菱形，则原四边形（　　）                  A．一定是矩形            B．一定是菱形                                                C．对角线一定互相垂直                                  D．对角线一定相等           答案：D【考点】中点四边形．                                                                           【分析】首先根据题意画出图形，由四边形EFGH是菱形，点E，F，G，H分别是边AD，AB，BC，CD的中点，利用三角形中位线的性质与菱形的性质，即可判定原四边形一定是对角线相等的四边形．                  【解答】解：如图，根据题意得：四边形EFGH是菱形，点E，F，G，H分别是边AD，AB，BC，CD的中点，                                                 ∴EF=FG=CH=EH，BD=2EF，AC=2FG，                                                  ∴BD=AC．                                                                                         ∴原四边形一定是对角线相等的四边形．                                                 故选：D．                                                                                                                                                           【点评】此题考查了菱形的性质与三角形中位线的性质．此题难度适中，注意掌握数形结合思想的应用．                     　                                                                                                      

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