1 . 如图,在五边形
中,
,点P,Q分别在边
,
上,连接
,
,
,当
的周长最小时,
的度数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6723f8b9d907981aa735cd96386bee36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834e64dbd62f3ca4b1475e54803af9d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128147bd4834566a78b4e9d2a3b2139c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/11f9f959-20f1-4b8e-93c1-ef373833720a.png?resizew=156)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 如图,已知
中,
,
,将
绕点
逆时针反向旋转
到
的位置,连接
,则
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bc7774144c164f7ebaeca54fa657e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7cf722ab91669117197c6a930e28b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f20e3745b76031e0bf6f5a4a860165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f20e3745b76031e0bf6f5a4a860165.png)
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21卷引用:重庆市南岸区第一一〇中学校2022-2023学年九年级上学期入学数学试题
重庆市南岸区第一一〇中学校2022-2023学年九年级上学期入学数学试题山东省济南市历下区2017-2018学年八年级(下)期末数学试卷(已下线)2018年9月16日 《每日一题》人教上 - 每周一测江西省广丰县丰溪街道南屏中学2019届九年级上学期第一次检测数学试题(已下线)2019年9月15日《每日一题》每 周 一测山东省日照市东港区日照港中学2020-2021学年九年级上学期期中数学试题广东省深圳市育才二中2020~2021学年八年级下学期数学期中测试试题广东省深圳市光明区光明中学2021-2022学年八年级下学期期中数学试题广东省茂名市茂南区2021-2022学年八年级下学期期中数学试题(已下线)专题23.10《旋转》全章复习与巩固(培优篇)(专项练习)-2022-2023学年九年级数学上册基础知识专项讲练(人教版)广东省广州市育才中学2022-2023学年九年级上学期第一次月考数学试卷新疆维吾尔自治区乌鲁木齐市第四十四中学2022-2023学年九年级上学期期中数学试题山东省临沂市兰山区临沂第六中学2022-2023学年九年级上学期期中数学试题广东省广州市中山大学附属中学2022—2023-学年九年级上学期数学期中考试卷广东省汕头市林百欣中学2022-2023学年九年级上学期数学科期中综合素质摸查试题(已下线)专题9.4 图形的旋转(培优篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(苏科版)(已下线)专题3.8 图形的旋转(培优篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(北师大版)(已下线)难点特训(五)选填压轴50道-【微专题】2022-2023学年八年级数学下册常考点微专题提分精练(北师大版)(已下线)9.1 图形的旋转-2022-2023学年八年级数学下册《考点·题型·技巧》精讲与精练高分突破系列(苏科版)广东省广州市南奥实验学校2022-2023学年九年级上学期月考数学试题广东省佛山市禅城区明德中英文学校2023-2024学年八年级下学期月考数学试题
名校
3 . 如图,在等腰三角形
中,
平分
垂直平分
交
于点
,则
的长是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029222a5dff22df03218fc4c76f73c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933926a18552f8a3b9cd6ab28212e1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
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5卷引用:重庆市北碚区2023-2024学年八年级上学期期末数学试题
4 . 如图,在直角三角形中,
的垂直平分线交
于
,交
的角平分线于
,连接
、
,若
的周长为
,则
的长度是( )
A.![]() | B.10 | C.12 | D.13 |
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3卷引用:重庆市北碚区2023-2024学年八年级上学期期末数学试题
重庆市北碚区2023-2024学年八年级上学期期末数学试题重庆市云阳县路阳镇路阳小学2023-2024学年八年级下学期3月月考数学试题(已下线)专题1.17 三角形的证明(全章知识梳理与核心考点分类讲解)-2023-2024学年八年级数学下册基础知识专项突破讲与练(北师大版)
名校
5 . 下列命题正确的是( )
A.一组对边平行,另一组对边相等的四边形是平行四边形 |
B.等腰三角形的高、中线、角平分线,三线合一 |
C.斜边相等的两个直角三角形全等 |
D.到一条线段两个端点距离相等的点,在这条线段的垂直平分线上 |
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3卷引用:重庆市北碚区西南大学附属中学校2023-2024学年八年级上学期期末数学试题
6 . 如图,在
中,
的角平分线交
于点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/6f35520b-9cfc-4456-9b2d-d572cae26cf1.png?resizew=186)
(1)用尺规完成以下基本作图:作
的垂直平分线分别与
、
、
交于点E、点F、点H.(保留作图痕迹,不写作法)
(2)在(1)所作的图形中,连接
、
,完成下面证明
的过程.
证明:∵
的角平分线交
于点D,
∴
①______.∵
垂直平分
,
∴
,
②______,
,
∴③______,∴
,
∴
④______
.∴
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/6f35520b-9cfc-4456-9b2d-d572cae26cf1.png?resizew=186)
(1)用尺规完成以下基本作图:作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)在(1)所作的图形中,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f43ee6bef36a3a67b497cb2e67f4df.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0c46783b77cce2bd4b45b9acc61884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4790b2cd75df9633fe25e9df427cc441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e776314d1f1670d3a90f2a35125feb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d00572a90232e08932317af2a53767.png)
∴③______,∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28580daa12f77508922012510f533db.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0780d075235fe5a85b550d06df0edef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14d38442c3e6967a6dca78b4d79dd0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f43ee6bef36a3a67b497cb2e67f4df.png)
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7 . 如图,已如
中,
平分
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/e764cabe-c51b-4589-92b8-1eeabed5b593.png?resizew=195)
(1)用尺规完成以下基本作图:作线段
的垂直平分线,分别交
、
、
于点
、
、
,连接
;(不写作法,保留清晰的作图痕迹)
(2)求证:
,请根据下列证明思路完成填空:
证明:
平分![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
①
是线段
的垂直平分线,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
,
在
和
中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45abcc39ca0b8c65e5cb4e7b006d8f0e.png)
(③ ).
④
是线段
的垂直平分线,
⑤
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ead683c30937825ab5fb9318265ac9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/e764cabe-c51b-4589-92b8-1eeabed5b593.png?resizew=195)
(1)用尺规完成以下基本作图:作线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d1125b47dec1c5e93143ee59ad862a.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d558048f4591f82e669ae89e20ebc082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173f7d26d069c0f16a0f6fcb517aa28c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d2b8c118073d36468e80d3ce9a0550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0cbf8d91c8197cb3ac9b2ddcc62daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1377ebe320b37246af7bd578663493fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45abcc39ca0b8c65e5cb4e7b006d8f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3802a9d87729fdf1f8c12931e174b8cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173f7d26d069c0f16a0f6fcb517aa28c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f96d400f5d5f0a40f17048dc0fa480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e879350fafa58e3ee192076c9ee3375.png)
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8 . 如图,
为
的高,
的垂直平分线
与
、
分别交于点
,
平分
.若
,则以下结论:①
;②
平分
;③
;④
.其中结论正确的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/5e4d6308-b8f7-47c8-8b61-9f4a1004c822.png?resizew=194)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c741cf8348e9fa4ee6894ac2c3ac6dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7e48723871f06a6aeae31a2a1ff79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2710d1ae999c3297ce2b89c93754a462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6344778ed1e75c1a99e2268468081867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f659a63da4c173cc2239ee53499952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be326bec72dfcc7bd6c3ffca0107582e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/5e4d6308-b8f7-47c8-8b61-9f4a1004c822.png?resizew=194)
A.1个 | B.2个 | C.3个 | D.4个 |
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名校
9 . 在学习了矩形后,小雨借助尺规找到了直角三角形斜边的中点,通过倍长中线构造了矩形,然后利用矩形对角线的性质探究出了直角三角形斜边上的中线与斜边的数量关系.请根据她的思路完成以下作图与填空:
中,
,用直尺和圆规,作
的垂直平分线交
于点
,垂足为点
,连接
并延长,在射线
上截取
,连接
、
.(不写作法,保留作图痕迹)
(2)在(1)问所作的图形中,求证:
.
证明:∵
垂直平分
,
∴点
是
的中点.
∴
_____.
∵
,
∴四边形
是平行四边形.
∵
_____,
∴四边形
是_____.
∴_____.
∵
,
∴
_____.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce05f91ce17863abc8a5a8f6002b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)在(1)问所作的图形中,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc58dc365e8bb140a95746bbfb5abb6.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
∴点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/721e20e19fe1d10bb8b0b91d8bd64f59.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0866e1551b61074ca8e61261ecd1f9dc.png)
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc889d8f4ad193a0502b83f694218f14.png)
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
∴_____.
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3403d60432af374950a237b9d5bd6b.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba212f92f415f3dd4a53b4962130a187.png)
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2024-01-14更新
|
191次组卷
|
4卷引用:重庆市九龙坡区育才中学校2023-2024学年九年级上学期期中数学试题
重庆市九龙坡区育才中学校2023-2024学年九年级上学期期中数学试题重庆市九龙坡区2023-2024学年九年级上学期第二次名校联考数学试题(已下线)中考重点01 尺规作图+补全证明过程(5题型+满分技巧+限时检测)-2024年中考数学【热点·重点·难点】专练(重庆专用)(已下线)专题9.19 矩形(题型分类拓展)-2023-2024学年八年级数学下册基础知识专项突破讲与练(苏科版)
10 . 如图,在
中,
,
于点
,
,
,点
为
边上的动点,点
为
边上的动点,则
的最小值是____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8817091d0f4b7d7ac6df560cb63c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f01c4faacedfe56f5127d6c0cc63cf.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2edc74248b3e3b205afc8e0a21478ef1.png)
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