名校
1 . 如图,在正方形
中,点
的坐标分别是
,
,点
在抛物线
的图象上,则
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b00c9499415c5801c64a8177f4b35e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc51e325e65de188652a802254adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c9800e4b992044d16681e77ff6563c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-16更新
|
271次组卷
|
6卷引用:吉林省长春市南关区东北师大附中明珠学校2022-2023学年九年级上学期期中数学试题
吉林省长春市南关区东北师大附中明珠学校2022-2023学年九年级上学期期中数学试题2024年广东省龙湖区新溪街道中考一模数学试题2024年广东省珠海市第十一中学中考一模数学试题(已下线)2024年广东中考数学模拟预测卷03-2024年中考数学【热点·重点·难点】专练(广东专用)2024年湖北省黄石市黄石港区部分学校中考一模数学试题2024年广东省东莞市可园中学九年级中考三模数学试题
名校
2 . 如图,正方形
的对角线相交于点O,点O又是另一个正方形
的一个顶点.若两个正方形的边长均为2,则图中阴影部分图形的面积为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c29feba6e7ec88196414dcd7d9ba68e.png)
您最近一年使用:0次
2024-04-13更新
|
197次组卷
|
10卷引用:吉林省长春外国语学校2021-2022学年八年级下学期数学第一阶段综合练习题
吉林省长春外国语学校2021-2022学年八年级下学期数学第一阶段综合练习题2022年新疆乌鲁木齐市第六十八中学中考数学模拟试卷(已下线)吉林省吉林市磐石市2023-2024学年九年级上学期期末数学试题江西省宜春市高安市第二中学、高安市吴有训实验学校2022-2023学年八年级下学期5月月考数学试题江西省上饶市余干县2022-2023学年八年级下学期第三次月考数学试题广东省茂名市崇文学校2023-2024学年九年级上学期期中数学试题(已下线)第04讲 正方形的性质和判定(知识解读+达标检测)-2023-2024学年八年级数学下册《知识解读·题型专练》(人教版)(已下线)第06讲 正方形的性质和判定(知识解读+达标检测)-2023-2024学年八年级数学下册《知识解读·题型专练》(苏科版)(已下线)第05讲 正方形(3个知识点+5类热点题型讲练+习题巩固)-【帮课堂】2023-2024学年八年级数学下册同步学与练(人教版)(已下线)第03讲 正方形的性质和判定(知识解读+达标检测)-2023-2024学年八年级数学下册《知识解读·题型专练》(浙教版)
名校
3 . 问题引入:
(1)如图1,
,
,
,E是线段
的中点,连接
并延长交
于点F,连接
.则
与
之间的数量关系是______;
问题延伸:
(2)如图2,在正方形
和正方形
中,点A、B、E在同一条直线上,点G在
上,P是线段
的中点,连接
、
.
①判断
与
之间的数量关系,并说明理由;
②连接
,若
,
,求
的长.
(1)如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1d0734d6cb1c8fdf1d519e42cf3ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b6d19fedaf8488f9637cd64efbca83.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/f52a58fbaf4fea03567e88a9f0f6e37e.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
问题延伸:
(2)如图2,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc7ee0ef8945ba1b90e59aed7cab889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87261df80b82221732329b6ef3fdda7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
2024-01-29更新
|
221次组卷
|
12卷引用:2022年吉林省长春市宽城区九年级数学第二次质量检测试题
2022年吉林省长春市宽城区九年级数学第二次质量检测试题陕西省咸阳市永寿县2022-2023学年九年级上学期期中数学试题(已下线)第一次阶段性测试-【单元测试】2022-2023学年八年级数学下册分层训练AB卷(苏科版)2023年山东省烟台地区中考一模数学试题(已下线)期末压轴题专训40题(第十六、十七、十八、十九、二十章)-2022-2023学年八年级数学下册同步考点知识清单+例题讲解+课后练习(人教版)福建省福州市三牧中学2022-2023年学年八年级下学期期末数学试题广东省云浮市新兴县水台中学2022-2023学年八年级下学期期中数学试题2024年湖北省黄冈市部分学校中考二模数学试题(已下线)人教版八下期中真题精选(常考60题18个考点分类专练)-2023-2024学年八年级数学下学期期中考点大串讲(人教版)2024年湖南省永州市冷水滩区李达中学八年级下学期期中数学试题(已下线)期末真题必刷05(压轴大题60题12个考点专练)-2023-2024学年八年级数学下学期期末考点大串讲(人教版)2024年湖北省黄石市下陆区部分学校中考模拟数学试题
4 . 如图,以锐角
的边
为边向外作正方形
和正方形
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/206ead90-2ca1-498b-ba08-43bcba7d95df.png?resizew=268)
(1)求证:
;
(2)图中
可以通过一次变换得到
,请你说出变换过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f279d402050043751e941f3bd7aaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddcd5435b39971f897210aa0b66a259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5541d498cf8a609c87ec3a82006addcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/206ead90-2ca1-498b-ba08-43bcba7d95df.png?resizew=268)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ca73acec7d14722867175b6cbc53fa.png)
(2)图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09a769a75b107390b9eeccc929f761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55bd1ad9e6d1bb7403eff61ad2b10b4.png)
您最近一年使用:0次
2023-03-07更新
|
165次组卷
|
4卷引用:吉林省四平市双辽市2022-2023学年九年级上学期期中数学试题
5 . 某数学兴趣小组在数学课外活动中,对多边形内两条互相垂直的线段做了如下探究:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/3fe243f5-2f5c-46fc-99b5-a4350b1f7403.png?resizew=467)
【观察与猜想】
(1)如图①,在正方形
中,点
、
分别是
、
上的两点,连接
,
,
,则
的值为___________.
【类比探究】
(2)如图②,在矩形
中,
,
,点
是边
上一点,连接
,
,且
,求
的值.
【拓展延伸】
(3)如图③,在
中,
,点
在
边上,连结
,过点
作
于点
,
的延长线交
边于点
.若
,
,
,则
___________.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/3fe243f5-2f5c-46fc-99b5-a4350b1f7403.png?resizew=467)
【观察与猜想】
(1)如图①,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.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/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8120f2eeb724c756b5f84a14c6df527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d270df3e3824d4ab5b018da3b202814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ada5e380d6b5b2066e34497e5f0baf0.png)
【类比探究】
(2)如图②,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b6e6b9a38932e653e053f1895b1bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee82a25c3ccc4bd94f3f528ff3e95713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ff04770f0235c89ff9953cc8a5b656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8775dcf60ad143bc59a58b000f374c56.png)
【拓展延伸】
(3)如图③,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7281b641656a5992abaafb4190ca9afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83e7c8586eef5596aef5fb5160a196a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9df6a61c453b50f0fea4f4f640df45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd0c00f62c22e90e7d542a2f8dd83d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc9f0779b0ba2f9f97caf35c166ad24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5697930f9fde7109b23307db66c9c7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dab383e32c3908af8a10515366654da.png)
您最近一年使用:0次
6 . 【探究问题】(1)阅读并补全解题过程
如图①,在四边形
中,
,点E是边
的中点,
.
求证:
平分
.
张某某同学受到老师说过的“有中点,延长加倍构造全等”的启发,延长
交射线
于点F,请你依据该同学的做法补全证明过程.
证明:延长
交射线
于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/bc39440c-c0d1-4d03-a97f-15ad74246821.png?resizew=414)
【应用】(2)如图②在长方形
中,将
沿直线
折叠,若点B恰好落在边
的中点E处,直接写出
的度数.
【拓展】(3)如图③在正方形
中,E为边
的中点,将
沿直线
折叠,点A落在正方形
内部的点F处,延长
交
于点G,延长
交
于点H,若正方形
的边长为4,直接写出
的值.
如图①,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc5653b8818c02e71dc54027b175256.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
张某某同学受到老师说过的“有中点,延长加倍构造全等”的启发,延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
证明:延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/bc39440c-c0d1-4d03-a97f-15ad74246821.png?resizew=414)
【应用】(2)如图②在长方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36719f1e764ee0e719b65c49fae84677.png)
【拓展】(3)如图③在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
您最近一年使用:0次
2023-01-30更新
|
212次组卷
|
2卷引用:吉林省长春市南关区第一O三中学校2022-2023学年八年级上学期期末数学试题
7 . 【提出问题】在一次数学探究活动中,李老师给出了一道题.如图①,点P是等边
内的一点,连接
、
、
.当
,
,
时,求
的度数.
【解决问题】小明在解决此题时,将点P绕点B逆时针方向旋转
得到点D,连接
、
、
,并结合已知条件证得
.
请利用小明的作法及结论求
的度数.
【方法应用】如图②,点P是正方形
内一点,连接
、
、
.若
,
,
,则
______°.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b336e518ac4ff04c6c26e4b8a15844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43c2d5aae759fc4db16115c8188ceec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
【解决问题】小明在解决此题时,将点P绕点B逆时针方向旋转
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae93d5ab92ceacc86bf646721ff6c35.png)
请利用小明的作法及结论求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
【方法应用】如图②,点P是正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3643fbbf4e0775dea240dff8fd6dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6b50b8b9011f2d7d1f3de2526796e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437edc71c77dbb17d84dbbb84ac1785b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a84b7de4bcbaa36f542b7ac3886bba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/2b553fa6-f2f4-4aa5-a02c-6753b286e879.png?resizew=325)
您最近一年使用:0次
8 . 【教材呈现】如图是华师版九年级上册数学教材第77页的部分内容:
如图,在
中,点
分别是
与
的中点,可以猜想:
且
.请写出证明过程.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/2afc9359-a886-428c-8265-6212e7aca094.png?resizew=418)
【结论应用】
(1)如图1,四边形
中,
,
分别是
的中点.若
,
,求
的度数.
(2)如图2,在
外分别作正方形
和
,
是
的中点,
分别是正方形的中心,
,则
的面积最大值为 .
如图,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.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/1d021981c03e75b1a246d899dcc64656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950e82a0f9712457f2dd9f8a93f8a217.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/2afc9359-a886-428c-8265-6212e7aca094.png?resizew=418)
【结论应用】
(1)如图1,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d2530e7023b2345c651e8f53629ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6241f9ef86cd0a902cbadaf336767dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f5ad4b4e38f664f9f0e880e7335690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67caa956042197d36d651c4ec1a75b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dd359121976a4f6dad70d4bfaad30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ca0ea573af39647bbb44977ed1eeb2.png)
(2)如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea61ea3f3cf0e3001a5094960e9dc11f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d98ce33701398fb190bf53707901cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999c42a021bdc576f097246b9e64d986.png)
您最近一年使用:0次
21-22八年级下·四川·期中
解题方法
9 . 已知,如图1,四边形
是正方形,
,
分别在边
、
上,且
,我们把这种模型称为“半角模型”,在解决“半角模型”问题时,旋转是一种常用的方法.
,为了证明结论“
”,小亮将
绕点
顺时针旋转
后解答了这个问题,请按小亮的思路写出证明过程;
(2)如图2,当
绕点
旋转到图2位置时,试探究
与
、
之间有怎样的数量关系?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192155e6a3aade305b76b1eb7c75e30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9af98a1a048b1e2f7c71e83c33498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c4e4adfae8ba95104a7f3e4de38bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e31edc5b71c488ca9942d70d9298f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
2022-11-11更新
|
625次组卷
|
10卷引用:吉林省松原市前郭县乌兰塔拉中学等五校联考2022-2023学年九年级上学期期中数学试题
吉林省松原市前郭县乌兰塔拉中学等五校联考2022-2023学年九年级上学期期中数学试题(已下线)四川省成都市金牛区金牛中学等五校联考2021-2022学年八年级下学期期中数学试题广东省惠州市小金茂峰学校2022-2023学年九年级上学期数学期中考试卷山东省德州市陵城区2022-2023学年九年级上学期期中数学试题陕西省宝鸡市凤翔县2022-2023学年九年级上学期第一次月考数学试题广东省河源广赋创新学校2021-2022学年八年级下学期期中模拟数学试题(已下线)专题3.2 旋转中的重要模型 专题讲练-2022-2023学年八年级数学下册重难题型全归纳及技巧提升专项精练(北师大版)(已下线)专题12.29 通过作辅助线证明三角形全等方法与技巧(分层练习)(综合练)-2023-2024学年八年级数学上册基础知识专项突破讲与练(人教版)(已下线)专题1.29 通过作辅助线证明三角形全等方法与技巧(分层练习)(综合练)-2023-2024学年八年级数学上册基础知识专项突破讲与练(苏科版)(已下线)专题4.20 三角形全等几何模型(半角模型)(培优练)-2023-2024学年七年级数学下册基础知识专项突破讲与练(北师大版)
名校
10 . 【推理】如图①,在边长为10的正方形
中,点
是
上一动点,将正方形沿着
折叠,点
落在点
处,连接
,
,延长
交
于点
.求证:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/6757e956-50a5-42f1-940e-e58e7b901e44.png?resizew=525)
【运用】如图②,在【推理】条件下,延长
交
于点
.若点
是
的中点,则线段
______.
【拓展】如图③,在【推理】条件下,
,
交于点
,取
的中点
,连接
,则
的最小值是______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995bd3b79d7864106b9804c7f23ea501.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/6757e956-50a5-42f1-940e-e58e7b901e44.png?resizew=525)
【运用】如图②,在【推理】条件下,延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080cf75e431b06c2ce435a3e15f7481b.png)
【拓展】如图③,在【推理】条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
您最近一年使用:0次