题目

如图，已知矩形ABCD中，R、P分别是DC、BC上的点，E、F分别是AP、RP的中点，当P在BC上从B向C移动而R不动时，那么下列结论成立的是（　　）                                                                                                                             A．线段EF的长逐渐增大                                B．线段EF的长逐渐减小         C．线段EF的长不改变                                   D．线段EF的长不能确定         答案：C【分析】因为R不动，所以AR不变．根据中位线定理，EF不变．               【解答】解：连接AR．                                                                           因为E、F分别是AP、RP的中点，                                                          则EF为△APR的中位线，                                                                       所以EF=AR，为定值．                                                                         所以线段EF的长不改变．                                                                        故选：C．                                                                                                                                                                  【点评】本题考查了三角形的中位线定理，只要三角形的边AR不变，则对应的中位线的长度就不变．                   　                                                                                                      

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