．如图，矩形ABCD的对角线AC，BD相交于点O，若AB=AO，求∠ABD的度数．�

．如图，矩形ABCD的对角线AC，BD相交于点O，若AB=AO，求∠ABD的度数．                   

【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．