已知:如图,△ABC.
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990549246918656/2990785007771648/STEM/532b5382-e862-4b82-8f51-4276c0cb296f.png?resizew=193)
求作:点D(点D与点B在直线AC的异侧),使得DA=DC,且∠ADC+∠ABC=180°.
作法:①分别作线段AC的垂直平分线l1和线段BC的垂直平分线l2,直线l1与l2交于点O;
②以点O为圆心,OA的长为半径画圆,⊙O与l1在直线BC上方的交点为D;
③连接DA,DC.
所以点D就是所求作的点.
(1)使用直尺和圆规,依作法补全图形(保留作图痕迹);
(2)完成下面的证明.
证明:连接OA,OB,OC.
∵直线l1垂直平分AC,点O,D都在直线l1上,
∴OA=OC,DA=DC.
∵直线l2垂直平分BC,点O在直线l2上,
∴______=______.
∴OA=OB=OC.
∴点A,B,C都在⊙O上.
∵点D在⊙O上,
∴∠ADC+∠ABC=180°.(______)(填推理的依据)
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990549246918656/2990785007771648/STEM/532b5382-e862-4b82-8f51-4276c0cb296f.png?resizew=193)
求作:点D(点D与点B在直线AC的异侧),使得DA=DC,且∠ADC+∠ABC=180°.
作法:①分别作线段AC的垂直平分线l1和线段BC的垂直平分线l2,直线l1与l2交于点O;
②以点O为圆心,OA的长为半径画圆,⊙O与l1在直线BC上方的交点为D;
③连接DA,DC.
所以点D就是所求作的点.
(1)使用直尺和圆规,依作法补全图形(保留作图痕迹);
(2)完成下面的证明.
证明:连接OA,OB,OC.
∵直线l1垂直平分AC,点O,D都在直线l1上,
∴OA=OC,DA=DC.
∵直线l2垂直平分BC,点O在直线l2上,
∴______=______.
∴OA=OB=OC.
∴点A,B,C都在⊙O上.
∵点D在⊙O上,
∴∠ADC+∠ABC=180°.(______)(填推理的依据)
更新时间:2022-05-30 22:30:35
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