名校
1 . 如图,在
中,
,E为
边的中点.
为边在
外部作等边
,连接
,
;(不写作法,保留作图痕迹)
(2)判断
的形状并给予证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0005e1ef60f6ddc5f9a83e3de1ef3b2e.png)
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2 . 如图1,在矩形
中,
,
是
边上一点,将
沿着直线
折叠,得到
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/6d9582f9-5371-4cd8-99f1-7946e78e623f.png?resizew=477)
(1)请在图2上仅用圆规,在
边上作出一点
,使
三点在一直线上(不写作法,保留作图痕迹),此时
的长为_____;
(2)请在图3上用没有刻度的直尺和圆规,在
边上作出一点
,使
平分
(不写作法,保留作图痕迹).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/758a7f13073799598447e9d0953ff510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48775f13f05443e6f6d30ae26e669f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/6d9582f9-5371-4cd8-99f1-7946e78e623f.png?resizew=477)
(1)请在图2上仅用圆规,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a6818ec36e9f6bee7484f57fc48b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
(2)请在图3上用没有刻度的直尺和圆规,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404fc19da3e4da41e9147e9f0ca64957.png)
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名校
3 . 已知:如图,点
在
的边
上.小樱根据要求进行尺规作图,请你依据小樱的作图痕迹回答下列问题.
是
的______;
(2)以点
为圆心、
长为半径画弧,交射线
于点
,连接
,试判断
与
的位置关系并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
(2)以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
您最近一年使用:0次
2024-03-29更新
|
269次组卷
|
3卷引用:2024年湖南省长沙市部分学校中考三模数学试题
2024年湖南省长沙市部分学校中考三模数学试题(已下线)抢分通关05 几何作图问题(含无刻度作图,2易错12题型)-备战2024年中考数学抢分秘籍(全国通用)广东省梅州市兴宁市第一中学2023-2024学年七年级上学期第二次月考数学试题
4 . 已知:点
和直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
求作:以点
为直角顶点的等腰直角三角形,使它的斜边落在直线上,并在三角形内部做出以斜边中点为圆心的面积最大的半圆
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
求作:以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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5 . 如图,在
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/12/1445c538-62d2-411f-adbe-fd589f05f0d1.png?resizew=151)
(1)
的面积等于_______.
(2)D为
的中点,P是
上的动点,连接
,
.当
取得最小值时,请在如图所示的矩形区域内,用无刻度的直尺和圆规,画出点P;并简要说明点P的位置是如何找到的.(保留作图痕迹,不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/12/1445c538-62d2-411f-adbe-fd589f05f0d1.png?resizew=151)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)D为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365822bd3945e6a3e871ca979c84cc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0d68882d58da4a445793d1c1a6f4e9c.png)
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6 . 已知等腰直角三角形
如图所示放置,根据题目要求补全图形,并保留作图痕迹.
①作点
关于线段
的对称点点
.
②在
延长线上取得一点
,连接
,并以点
为直角顶点,线段
为直角边作等腰直角三角形
.
③连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/aebf389f-6413-4c13-a94a-3e25a0eff59f.png?resizew=159)
(1)找出补全后图中与
全等的三角形,并给予证明(说明:结论中不得含有未标识的字母);
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdd615843adf3e011e5b72f9c608bfa.png)
①作点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2194add18a7df1a23cf1554dc2da1b40.png)
③连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/aebf389f-6413-4c13-a94a-3e25a0eff59f.png?resizew=159)
(1)找出补全后图中与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b59bfa454f1729db06a42362086230f.png)
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7 . 在
中,
,直线 l 经过点 A,且与
平行.仅用圆规和无刻度的直尺完成下 列画图.(保留画图痕迹,不写作法)
;
(2)如图②,在直线 l 上画出所有的点 Q,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c65edad25ddd666cdce0d7e5afefc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effa7cd45df3d07ce54a34e2c56a04b1.png)
(2)如图②,在直线 l 上画出所有的点 Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc5c733915252fb763d23a8fcc1de9d.png)
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8 . 在
中,
,直线
经过点
,且与
平行.请用不带刻度的直尺和圆规完成下列作图.(保留作图痕迹,不写作法)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/454e4359-02ae-4f9c-8537-4ef9416d518f.png?resizew=414)
(1)如图①,在直线l上作出一点P,使得
;
(2)如图②,在直线
上作出所有的点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/454e4359-02ae-4f9c-8537-4ef9416d518f.png?resizew=414)
(1)如图①,在直线l上作出一点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09a88dc7dc9cd668a57138e1ec71ea2.png)
(2)如图②,在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a756ab9d2f4d457fe8ac4ada62824c6.png)
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9 . 已知线段a、b.求作等腰三角形
,使底边
,底边上的高
.(要求用尺规作图,不写作法,保留作图痕迹)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0786732df29e599cd67cd69e5a1a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/aa7a8e5e-56a8-46d8-913f-ec2d67b35979.png?resizew=141)
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10 . 如图,已知线段
,求作等腰三角形
,使底边AB的长为
,底上高的长为
(不写作法,保留作图痕迹).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9699a430612289f93365ab3a238470c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/e26422cd-9c9c-4cb9-b8b5-705b182a196b.png?resizew=328)
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