如图,在10×10的正方形网格中,每个小正方形的边长都为1(即三角形的顶点都在格点上).
(1)在图中作出
ABC关于直线l对称的
A1B1C1;(要求:A与A1,B与B1,C与C1相对应)
(2)若有一格点P到点A、B的距离相等(PA=PB),则网格中满足条件的点P共有多少个;
(3)在直线l上找一点Q,使QB+QC的值最小.
(4)如图已知∠AOB和C、D两点,求作一点P,使PC=PD,且P到OA的距离等于P到OB的距离.
![](https://img.xkw.com/dksih/QBM/2021/10/14/2829232992411648/2829942527901696/STEM/a26d13c7-8387-454a-8035-8308f8fa8db3.png)
(1)在图中作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
(2)若有一格点P到点A、B的距离相等(PA=PB),则网格中满足条件的点P共有多少个;
(3)在直线l上找一点Q,使QB+QC的值最小.
(4)如图已知∠AOB和C、D两点,求作一点P,使PC=PD,且P到OA的距离等于P到OB的距离.
![](https://img.xkw.com/dksih/QBM/2021/10/14/2829232992411648/2829942527901696/STEM/a26d13c7-8387-454a-8035-8308f8fa8db3.png)
![](https://img.xkw.com/dksih/QBM/2021/10/14/2829232992411648/2829942527901696/STEM/66472aec-654f-454d-b7d8-c8a5445a731a.png?resizew=130)
更新时间:2021-10-15 16:35:43
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解答题-作图题
|
适中
(0.65)
【推荐1】如图,在长方形
中,
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,将长方形
沿直线
折叠(点
是折痕和边
的交点),使点
落在
上的
处.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/79046be3-8f21-4ef7-8c23-9330baf981c0.png?resizew=148)
(1)请你利用尺规作图确定点
和点
.(保留作图痕迹,不写做法)
(2)将图形补充完整,
______.
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(1)请你利用尺规作图确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)将图形补充完整,
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解答题-证明题
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名校
【推荐2】如图,四边形
是平行四边形,
平分
交
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,
交
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,连接
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与
的位置关系,并证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/1/dac72a5f-c392-4ed4-bd66-cb5a0c6e1c39.png?resizew=150)
(1)补全图形;
(2)
与
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(3)证明:_____________
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(1)补全图形;
(2)
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(3)证明:_____________
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解答题-作图题
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【推荐1】小明在学习了平行四边形后,对其进行了进一步的研究,发现如果作平行四边形任意一条对角线的垂直平分线,那么这条垂直平分线一定平分这个平行四边形的面积.他的思路是通过全等和图形的拼接得到面积相等.请根据思路完成以下作图与填空:
如图,在平行四边形
中,
.
的垂直平分线
交
于点E,交
于点F,垂足为O(保留作图痕迹,不写作法,不写结论);
(2)在(1)所作图形中,求证:
.
证明:
四边形
是平行四边形,
∴
,
,
①__________.
垂直平分
,
②__________.
又
③__________,
.
.
又
,
.
同理,
,
.
小明进一步研究发现,过平行四边形对角线中点的直线也有此特征.
请你依照题意完成下面命题:
过平行四边形对角线中点的直线④_____________________.
如图,在平行四边形
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6694f3443cc5f4d09948679251b61.png)
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(2)在(1)所作图形中,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30036de857df0fdfc0bf840449ba578.png)
证明:
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
∴
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又
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170fe589b2898df51cc44f5ad844b9d5.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9453e2fefe053c341004b49a23235ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182333bec6528fb597d77cb9fc8f9c02.png)
同理,
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小明进一步研究发现,过平行四边形对角线中点的直线也有此特征.
请你依照题意完成下面命题:
过平行四边形对角线中点的直线④_____________________.
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解答题-问答题
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【推荐2】如图,已知∠AOB和边OB上一点E,求作:一点P,使P到∠AOB两边的距离相等,且OP=EP.
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解答题-作图题
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适中
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【推荐1】如图,在长度为1个单位长度的小正方形组成的正方形网格中,点A、B、
在小正方形的顶点上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/086d1f4e-e35a-43b6-95c6-04660abb8163.png?resizew=196)
(1)在图中画出与
关于直线
成轴对称的△
;
(2)
的面积是 .
(3)在直线
上找一点
,使
的长最短.
(4)以
为边作与
全等的三角形,可作出 个三角形与
全等.
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/086d1f4e-e35a-43b6-95c6-04660abb8163.png?resizew=196)
(1)在图中画出与
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(2)
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(3)在直线
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(4)以
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解答题-作图题
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【推荐2】如图①,是由2个白色和2个阴影全等正方形组成的“L”型图案,请你分别在图②,图③上按下列要求画图.
(2)在图③中,先改变1个正方形的位置,再添1个白色或阴影正方形,使它既成中心对称图案,又成轴对称图案.
(2)在图③中,先改变1个正方形的位置,再添1个白色或阴影正方形,使它既成中心对称图案,又成轴对称图案.
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