题目

．如图，矩形ABCD的对角线AC，BD相交于点O，若AB=AO，求∠ABD的度数．                                                                                           答案：【解答】解：∵四边形ABCD是矩形，                                                     ∴OA=OC，OB=OD，AC=BD，                                                                ∴AO=OB，                                                                                        ∵AB=AO，                                                                                         ∴AB=AO=BO，                                                                                  ∴△ABO是等边三角形，                                                                         ∴∠ABD=60°．                                                                                                                                                         【点评】本题考查矩形的性质、等边三角形的判定和性质等知识，熟练掌握矩形的性质是解题的关键，属于基础题，中考常考题型．                                                                                        

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