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分析 先根据等边△OAD和等边△ABC的性质,得出∠OAD=∠BAC=60°,OA=DA,BA=CA,进而判定△OAB≌△DAC,最后根据全等三角形的性质,得出OB=DC. 解答 证明:∵等边△OAD和等边△ABC,∴∠OAD=∠BAC=60°,OA=DA,BA=CA,∴∠OAB=∠DAC,在△OAB和△DAC中,⎧⎪⎨⎪⎩OA=DA∠OAB=∠DACBA=CA{OA=DA∠...
10.在平面直角坐标系中.直角梯形AOBC的位置图所示.∠OAC=90°.AC∥OB.OA=4.AC=5.OB=6.M.N分别在线段AC.线段BC上运动.当△MON的面积达到最大时.存在一种使得△MON周长最小的情况.则此时点M的坐标为(3.4).
(1)将图1中∠COD绕O点逆时针旋转,使射线OC与射线OA重合(∠AOC=0°,ON与OA重合,如图2),其他条件不变,请直接写出∠MON的度数 ; (2)将图2中的∠COD绕O点逆时针旋转α度,其他条件不变. ①当40°<α<100°,请完成图3,并求∠MON的度数; ②当140°<α<180°,请完成图4,并求∠MON的度数. ...