1 . 已知
,
,
,点D为直线
上的一动点(点D不与B、C重合),以
为边作
(其中
,
,A、D、E按逆时针排列),连接CE.
(1)如图1,当点D在边
上时.
①请写出
和
之间存在数量关系和位置关系,并说明理由;
②
的关系是否成立,并说明理由;
(2)如图2,当点D在边
的延长线上且其他条件不变时,(1)中
之间存在的数量关系是否成立?若不成立,请直接写出
之间存在的数量关系,不证明;
(3)如图3,当点D在边
的延长线上且其他条件不变时,补全图形(要求:尺规作图,不写作法,保留作图痕迹),并直接写出
之间存在的数量关系,不证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e7ba6e267dde1a65a98f9f36b585ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d212c1709b8e72a055cf1b5381ef64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931b1589d78dd81a3ecac7b9664b3307.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/1530660a-315c-4ed1-bd28-0b9b2348504d.png?resizew=438)
(1)如图1,当点D在边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
①请写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dc65a3ffa7b8d05997af50613636c4.png)
(2)如图2,当点D在边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce31a6926224dd7ce32ab8c2d52dd352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce31a6926224dd7ce32ab8c2d52dd352.png)
(3)如图3,当点D在边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce31a6926224dd7ce32ab8c2d52dd352.png)
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2 . 如图,点O在∠ABC的边BC上,以OB为半径作⊙O,∠ABC的平分线BM交⊙O于点D,过点D作DE⊥BA于点E.
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987025049870336/2988295103250432/STEM/4248cae7-e30b-4e2c-a1e6-b42d7d40d4a5.png?resizew=192)
(1)尺规作图(不写作法,保留作图痕迹),补全图形;
(2)判断⊙O与DE交点的个数,并说明理由.
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987025049870336/2988295103250432/STEM/4248cae7-e30b-4e2c-a1e6-b42d7d40d4a5.png?resizew=192)
(1)尺规作图(不写作法,保留作图痕迹),补全图形;
(2)判断⊙O与DE交点的个数,并说明理由.
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3 . 如图,在
中,
,按以下步骤作图:
![](https://img.xkw.com/dksih/QBM/2021/11/29/2861731595165696/2863224996306944/STEM/502f094c-5c53-466e-b9f3-47c5ad1b0ad3.png)
①以点
为圆心,任意长为半径作弧,分别交边
,
于点
,
;
②分别以点
,
为圆心,大于
的相同长度为半径作弧,两弧交于点
;
③作射线
交
于点
.
(1)根据上述步骤补全作图过程(要求:尺规作图,不写作法,保留作图痕迹);
(2)过点
作
交射线
于点
,
,
.补全图形,并求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://img.xkw.com/dksih/QBM/2021/11/29/2861731595165696/2863224996306944/STEM/502f094c-5c53-466e-b9f3-47c5ad1b0ad3.png)
①以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
②分别以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65026a6b6402cb599e14be8023a3f6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
③作射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)根据上述步骤补全作图过程(要求:尺规作图,不写作法,保留作图痕迹);
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a74f478fb96f1c7e3ed3f8ad9078c06f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ebb33adb2310a6e03918761e68204a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
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4 . 如图,是小清同学的数学笔记,任细阅读并完成任务:
任务:
(1)填空:“办法一”中,判别四边形
是菱形的数学依据是_____;
(2)在图2中,根据“办法二”的作图方法,使用直尺和圆规补全图形(保留作图痕迹);
(3)写出“办法二”的推理过程.
在平行四边形![]() ![]() ![]() ![]() ![]() ![]() ![]() 办法一: 以点 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 办法二: 连接 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(1)填空:“办法一”中,判别四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
(2)在图2中,根据“办法二”的作图方法,使用直尺和圆规补全图形(保留作图痕迹);
(3)写出“办法二”的推理过程.
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2021-05-07更新
|
176次组卷
|
3卷引用:四川省达州市2023年中考数学模拟预测题(二)
5 . 如图,在
中,
,
,要把图纸上的这块三角形土地均分给甲、乙、丙三家农户,并使这三家农户所得土地的大小、形状都相同,请在图上画出分割图.(要求;尺规作图,要写出作法,并保留作图痕迹.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0f5353b4b4a463dffcef43db49ff3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191599d684f41efc62579911e29cbdf5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/4/fbdcd4a5-8e73-4cae-8796-e85955569890.png?resizew=173)
您最近一年使用:0次
名校
6 . 下面是小明设计的“在一个平行四边形内作菱形”的尺规作图过程.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/ccedcc30-2938-4312-a1eb-6cf27458112b.png?resizew=250)
已知:四边形
是平行四边形,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86ffe3ecbb59ce2b8f7c5b972a62efe.png)
求作:菱形
,使点
在
上,点
在
上.
作法:①作
的角平分线,交
于点
;
②以
为圆心,
长为半径作弧,交
于点
;
③连接
.
则四边形
为所求作的菱形.
根据小明设计的尺规作图过程
(1)使用直尺和圆规,补全图形(保留作图痕迹);
(2)求证四边形
为菱形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/ccedcc30-2938-4312-a1eb-6cf27458112b.png?resizew=250)
已知:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86ffe3ecbb59ce2b8f7c5b972a62efe.png)
求作:菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
作法:①作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
②以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
③连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
则四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
根据小明设计的尺规作图过程
(1)使用直尺和圆规,补全图形(保留作图痕迹);
(2)求证四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
您最近一年使用:0次
2021-02-07更新
|
114次组卷
|
2卷引用:四川省达州市开江县2020-2021学年九年级上学期期末数学试题
真题
7 . 如图,点O在
的边
上,以
为半径作
,
的平分线
交
于点D,过点D作
于点E.
(1)尺规作图(不写作法,保留作图痕迹),补全图形;
(2)判断
与
交点的个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62ca3d0dd0057a11181c43aeb6b40b6.png)
(1)尺规作图(不写作法,保留作图痕迹),补全图形;
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/5/c1dfadc9-0852-408b-900d-177f107b8b69.jpg?resizew=109)
您最近一年使用:0次
2020-07-17更新
|
853次组卷
|
4卷引用:四川省达州市2020年中考数学试题
四川省达州市2020年中考数学试题(已下线)考点18 尺规作图与定义、命题、定理-备战2021年中考数学考点 核心考点清单2021年甘肃省陇南市武都区九年级二模数学试题山东省烟台市海阳市2023-2024学年九年级上学期期末数学试题
8 . 如图所示,△ABC的顶点均在格点上,点C的坐标为(4,﹣1).
①将△ABC以绕原点O顺时针方向旋转90°得到对应的△A1B1C1,请画出△A1B1C1,并写出点B1的坐标;
②作出△ABC的外接圆,并计算△ABC的外接圆的面积.(要求:尺规作图,保留作图痕迹,不写作法)
①将△ABC以绕原点O顺时针方向旋转90°得到对应的△A1B1C1,请画出△A1B1C1,并写出点B1的坐标;
②作出△ABC的外接圆,并计算△ABC的外接圆的面积.(要求:尺规作图,保留作图痕迹,不写作法)
![](https://img.xkw.com/dksih/QBM/2022/1/1/2884881836515328/2887317558460416/STEM/84dc7ee1-0f42-44b1-8a3a-a718ad62c5d6.png?resizew=409)
您最近一年使用:0次
名校
9 . 先填空,后作图:
![](https://img.xkw.com/dksih/QBM/2021/3/24/2684785676156928/2685374555881472/STEM/4e2bdbf7d88044a7a0358eba25f5ed60.png?resizew=146)
(1)角的内部,到角两边距离相等的点,在它的______________上;
(2)到线段两端距离相等的点在它的_______________上;
(3)如图,两条公路
与
是两个村庄,现在要建一个菜市场P,使它到两个村庄的距离相等,同时到两条公路的距离也相等,用尺规作图画出菜市场P的位置(不写作法,保留作图痕迹).
![](https://img.xkw.com/dksih/QBM/2021/3/24/2684785676156928/2685374555881472/STEM/4e2bdbf7d88044a7a0358eba25f5ed60.png?resizew=146)
(1)角的内部,到角两边距离相等的点,在它的______________上;
(2)到线段两端距离相等的点在它的_______________上;
(3)如图,两条公路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98fb900191e655d659a996a50cfe66fb.png)
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2021-03-25更新
|
165次组卷
|
8卷引用:四川省眉山市东坡区百坡初级中学2020-2021学年八年级上学期第三次月考数学试题
名校
10 . 已知∠BAC,点D是AC边上一点,按要求画图,只保留作图痕迹,不写作图过程.
![](https://img.xkw.com/dksih/QBM/2021/3/13/2677264220602368/2682706190614528/STEM/c4987b17-eac8-4c16-9fd8-d3f584424925.png?resizew=215)
(1)用尺规作图在AC的右侧以点D为顶点作∠CDP=∠CAB;
(2)射线DP与AB的位置关系为 ,理由是 ;
(3)画出表示点D到AB 的距离的线段和表示点B到AC的距离的线段.
![](https://img.xkw.com/dksih/QBM/2021/3/13/2677264220602368/2682706190614528/STEM/c4987b17-eac8-4c16-9fd8-d3f584424925.png?resizew=215)
(1)用尺规作图在AC的右侧以点D为顶点作∠CDP=∠CAB;
(2)射线DP与AB的位置关系为 ,理由是 ;
(3)画出表示点D到AB 的距离的线段和表示点B到AC的距离的线段.
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2021-03-21更新
|
443次组卷
|
5卷引用:四川省巴中市巴中中学2017-2018学年七年级下学期期中数学试题
四川省巴中市巴中中学2017-2018学年七年级下学期期中数学试题广东省深圳市南山区南山外国语学校(集团)2020-2021学年七年级下学期期中数学试题(已下线)专题15 尺规作图特训-【微专题】2022-2023学年七年级数学下册常考点微专题提分精练(北师大版)(已下线)第一次月考押题培优卷(2)(考试范围:第一、二章)-【微专题】2022-2023学年七年级数学下册常考点微专题提分精练(北师大版)(已下线)2.4 用尺规作角-2022-2023学年七年级数学下册《考点·题型·技巧》精讲与精练高分突破系列(北师大版)