1 . 如图,在四边形
中,
是对角线,
是等边三角形.线段
绕点C顺时针旋转
得到线段
,连接
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989c75a3fd02e4971cab421c88de92f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2c34a83631c3127ca5896e00cda297.png)
![](https://img.xkw.com/dksih/QBM/2023/9/2/3316288945782784/3344363240341504/STEM/99064bcd6bc04008b8f2633f9177f656.png?resizew=174)
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2 . 如图,
和
都是等边三角形,连接
、
,延长E交
于F点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/ceb7d558-175c-45b4-9a85-58c38d7da030.png?resizew=163)
(1)证明:
.
(2)如果
绕点C转动,并且
,那么
是否随
的变化而变化?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/ceb7d558-175c-45b4-9a85-58c38d7da030.png?resizew=163)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0005e13fe362d29df0818956310f3bd.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50515b0461f55861fd28f2774a2f01dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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2023-10-02更新
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7卷引用:吉林省四平市公主岭市2022-2023学年九年级上学期第二次月考数学试题
吉林省四平市公主岭市2022-2023学年九年级上学期第二次月考数学试题河北省邯郸市凌云中学2022--2023学年九年级上学期期中数学试题(已下线)专题13.8 轴对称章末拔尖卷-2023-2024学年八年级数学上册举一反三系列(人教版)(已下线)专题2.9 轴对称图形章末拔尖卷-2023-2024学年八年级数学上册举一反三系列(苏科版)(已下线)专题13.11 全等三角形章末拔尖卷-2023-2024学年八年级数学上册举一反三系列(华东师大版)福建省龙岩市连城县冠豸片区2023-2024学年八年级上学期月考数学试题(已下线)专题15.8 轴对称图形与等腰三角形章末拔尖卷-2023-2024学年八年级数学上册举一反三系列(沪科版)
3 . 如图,在
中,
,D为直线
上一动点(不与点B,C重合),在
的右侧作
,使得
,
,连接
.
(1)当D在线段
上时,求证:
;
(2)当
时.
①若点D在线段
上,则
的形状为
②若
中的最小角为
,则
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30e50e094cd2849e38859b36aad0b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43651721f6c0ea4cf50a33054ecc5d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/30/f1fec3b5-8b4c-492b-9437-ac5a889728ce.png?resizew=161)
(1)当D在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc71a2c3f2159da7847f4c6350ad4a53.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28971fe3e3f9d3849400e98b46fc3ba.png)
①若点D在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aee6e4e9350a2665df8597ff8045bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb663fe83b1f7e93e13d91cc6460f9c.png)
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7卷引用:吉林省松原市宁江区三校2022-2023学年九年级下学期期中数学试题
吉林省松原市宁江区三校2022-2023学年九年级下学期期中数学试题辽宁省沈阳市皇姑区虹桥中学2023-2024学年九年级上学期开学考试数学试题(已下线)专题13.4 等边三角形的性质与判定【十大题型】-2023-2024学年八年级数学上册举一反三系列(华东师大版)(已下线)专题13.3 等边三角形的性质与判定【十大题型】-2023-2024学年八年级数学上册举一反三系列(人教版)(已下线)专题2.3 等边三角形的性质与判定【十大题型】-2023-2024学年八年级数学上册举一反三系列(浙教版)(已下线)专题2.3 等边三角形的性质与判定【十大题型】-2023-2024学年八年级数学上册举一反三系列(苏科版)(已下线)专题15.3 等边三角形的性质与判定【十大题型】-2023-2024学年八年级数学上册举一反三系列(沪科版)
4 . 如图所示,
与
相交于点O,且
,过点O作直线
交
于E,交
于F,试说明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee22c01858985502cdc052da85a03e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94190469ba2229faa6fdcc96841803da.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/14/922b6ea0-c35c-4c13-bcd7-619d3d8020bb.png?resizew=151)
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5 . 知识探究:如图1,点E是正方形
对角线AC上任意一点,以点E为直角顶点的直角
两边
,
分别角与
,
相交于M点,N点.当
时,请探究
与
的数量关系,并说明理由;
拓展探究:当
绕点E顺时针旋转到点M与点D重合时,如图2,请探究
与
的数量关系,并说明理由;
迁移运用:在图2的基础上,过点E作
于点H,如图3,证明H是线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](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/ab1a1fd2fc33e89f357cef772ff6cd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
拓展探究:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
迁移运用:在图2的基础上,过点E作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3bb34308698b377df58ef5441aeec76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/85b40302-90df-4c93-8d52-f4df9fe5b4ed.jpg?resizew=411)
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2023-09-19更新
|
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7卷引用:吉林省白山市浑江区第十六中学2023-2024学年九年级上学期期末数学试题
吉林省白山市浑江区第十六中学2023-2024学年九年级上学期期末数学试题吉林省吉林市船营区第五中学2023-2024学年九年级上学期期末数学试题(已下线)专题01 与旋转有关的计算(30题)-【帮课堂】2023-2024学年九年级数学上册同步学与练(人教版)(已下线)23 图形的旋转(题型精讲精练)-【题型分类精粹】2023-2024学年九年级数学上学期期中期末复习讲练系列【考点闯关】(人教版)(已下线)第1章 特殊平行四边形(单元测试·综合卷)-2023-2024学年九年级数学上册基础知识专项突破讲与练(北师大版)(已下线)专题07 图形的旋转与中心对称之七大题型-【好题汇编】备战2023-2024学年九年级数学上学期期末真题分类汇编(人教版)山东省泰安市岱岳区2022-2023学年八年级下学期期末数学试题
6 . 下面是小明同学的作业及自主探究笔记,请认真阅读并补充完整.
【作业】如图①,在
中,
,
,点
为线段
上一动点(不与端点
,
重合),以
为边在
的上方作正方形
,连接
,求证:
.
证明:
,
,
.
四边形
是正方形,
,
.
,
,
________.
又
,
,
________,
.
,
.
【探究】
(1)如图②,当点
在线段
的延长线上时,其他条件同上.请判断
、
和
三条线段之间的关系,并说明理由.
(2)如图③,当点
在线段
的反向延长线上时,且点A,
分别在直线
的两侧,其他条件同上,在正方形
中,对角线
、
相交于点
,若
,
,直接写出
的长.
【作业】如图①,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf0fa55b2728fbe1ddf8d3b33b07043.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/4/fe6268c9-f2a6-4b06-ad3e-f21c9118e942.png?resizew=166)
图①
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ca7645614c362363ce66f6811ebad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64fc9ccb4e9eb351b6ce1c3697a19d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595d7d9e3cf0f62e1d8167926abfd209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597221bdc3fdacf0b653e447330df351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bdb4ec1fb92d009bca16d378104716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a407583c48a4358f0a9892db1212c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da552dbed4bbb91fc8d66d06ed0ef8a.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fb9bc6163bd3f8aa1a8b0a70c9cbf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4e363bfd418579e6229230df034bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4009febdcbb2600e558dc4bfdd950cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2465905e3e20be86a6a993a511ef57a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7839a3658382d7f9b35f8fa4f017892b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffbf247d393f0d6c642a15eee20c927.png)
【探究】
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/4/48200962-83b8-4021-9ea7-52b24e1144b8.png?resizew=163)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/4/c0eb637a-8053-4bb7-a59a-431c2a3fcc34.png?resizew=158)
图② 图③
(1)如图②,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)如图③,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bdfb0e1be5583e794ab614a8abe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
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7 . 【感知】如图①,在
中,
,
是斜边
上的中线,求证:
.
小明的思路如下:证明:如图①,延长
至点
,使
,连结
,
结合图①,补全证明过程;
【拓展】
(1)如图②,在
中,
,
,点
,
分别是
,
的中点,连结
,
,且
,
,则
的长为______ .
(2)如图③,
和
中,
,
,
,点
在边
的延长线上,连结
,若
,
分别是
,
的中点,
,
,则
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71622531dfa894f21b2da123d020d24.png)
小明的思路如下:证明:如图①,延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa1aa5a7a5bb172ed4603f17c8b2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd97740e8f35c9c05f8bb53c0f1cb47.png)
【拓展】
(1)如图②,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](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/3b2731722026737ed98c7ef0e0842abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82773737609e65dea3c5c67099f1b10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)如图③,
![](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/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d212c1709b8e72a055cf1b5381ef64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26813466e2ee49a493881a4384fc8748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c3ec174b1ce835cc8737ff6ce57e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2b3247afa684b10c8e1da99cf33d5b.png)
您最近一年使用:0次
名校
8 . 问题发现:
(1)如图①,已知点
为线段
上一点,分别以线段
、
为直角边作等腰直角三角形,
,
,
,连接
、
,则
、
之间的数量关系为________,位置关系为________.
拓展探究:
(2)如图②,把
绕点
逆时针旋转,线段
、
交于点
,则
与
之间的关系是否仍然成立?请说明理由.
拓展延伸:
(3)如图③,已知
,
,
,连接
、
、
,把线段
绕点A旋转,若
,
,请直接写出旋转过程中线段
的最大值.
(1)如图①,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f8145e5b12aa0b0b13ce4d64c619ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d365cc7ce9022654091eee60bc1c2b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a291c43cfa0df7a643be250c0a5e233f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
拓展探究:
(2)如图②,把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ce5d6ca24e249f7172e51c154509b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
拓展延伸:
(3)如图③,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212bfbd5575772ca36d6fc3e7b246e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc7897e3f49075943704f4dbef82e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28aabb982ce85e5ed9399a5ca8e3658e.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/1/56c52d6f-8832-47ae-9ab7-d697ee0c3d9d.png?resizew=401)
您最近一年使用:0次
2023-08-27更新
|
145次组卷
|
7卷引用:吉林省吉林市龙潭区亚桥第二九年制学校2022-2023学年九年级上学期期中数学试题
9 . 图①、图②、图③均是
的正方形网格,每个小正方形的边长均为1,每个小正方形的顶点称为格点,
的顶点均在格点上,只用无刻度的直尺,在给定的网格中,分别按下列要求画图,保留作图痕迹.
(1)在图①中的
边上找到一点
,使
;
(2)在图②中找到一格点
,连接
,使
;
(3)在图③中找到一格点
,连接
,使
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd4be97adde17423d59d86d18318c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/e1a4b83e-4b1a-4508-9165-8345db22eedf.png?resizew=436)
(1)在图①中的
![](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/57eb33b3f1cf4d775e4d75368d4e96b4.png)
(2)在图②中找到一格点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8ba4da3a6b049f010c91ccb4f328ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e56c222c15e924079ccc0f4213ddb3f.png)
(3)在图③中找到一格点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb73ae3dc9f67bcf303e7c94a37080d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa6f7a440e027b540e0edd8f02410e0.png)
您最近一年使用:0次
10 . 已知图1是边长分别为a和b
的两个等边三角形纸片
和三角形
叠放在一起(C与
重合)的图形.
绕点C按顺时针方向旋转
,连接
,
.如图2:在图2中,线段
与
之间具有怎样的大小关系?证明你的结论;
(2)若将上图中的
,绕点C按顺时针方向任意旋转一个角度
,连接
、
,如图3:在图3中,线段
与
之间具有怎样的大小关系?证明你的结论:
(3)根据上面的操作过程,请你猜想当
为多少度时,线段
的长度最大,最大是多少?当
为多少度时,线段
的长度最小,最小是多少?请直接写出答案.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f638f57e9566b938633785bdd79c864c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d61b279d8e19b6f74a79d249d66fe4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549e807ed5636b783c51603d38337313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)若将上图中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549e807ed5636b783c51603d38337313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)根据上面的操作过程,请你猜想当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2023-08-09更新
|
170次组卷
|
12卷引用:吉林省松原市前郭县北片名校调研2023-2024学年九年级上学期期中数学试题
吉林省松原市前郭县北片名校调研2023-2024学年九年级上学期期中数学试题江苏省连云港市2017届九年级中考模拟(四)数学试题江苏省海安县曲塘中学附属初级中学2018届九年级11月学业质量分析与反馈数学试题黑龙江齐齐哈尔2020~2021学年九年级上学期期中考试数学试题黑龙江省齐齐哈尔市建华区2020-2021学年九年级上学期期中数学试题河南省驻马店市平舆县2022-2023学年九年级上学期期中数学试题河北省保定市第十九中学2018-2019学年八年级下学期期中数学试题甘肃省白银市景泰县第四中学2021-2022学年八年级下学期期中考试数学试题福建省宁德市博雅培文学校2022-2023学年八年级下学期期中数学试题广东省佛山市南海区桂江第一初级中学2020-2021学年八年级下学期4月月考数学试题湖南省娄底市双峰县2023-2024学年八年级上学期期末数学试题广东省揭阳市惠来县2023-2024学年八年级下学期期中数学试题