1 . (1)问题解决:如图1,点
在一条直线上,
,求证:
;
(2)问题探究:在(1)的条件下,若点
为
的中点,求证:
;
(3)拓展运用:如图2,在
中,
,点
是
的内心,若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460c70650cd64f4e9373c2120ac9a1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca25fc6bdeef740a0d0a904deaef0247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26610053492d1edb6392341fcc02a80.png)
(2)问题探究:在(1)的条件下,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0065aeea21c22fcf3f67ba8afdca0862.png)
(3)拓展运用:如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249cb151ca125f58c7cd13576134549b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e1dc96c83c7fa41ef14b647c011c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2 . 如图1,两个全等的直角三角形
和
的斜边
和
在同一直线上,
,将
沿直线
平移,并连接
,
.
【基础巩固】
(1)求证:在
沿直线
平移过程中,四边形
是平行四边形;
【操作思考】
(2)如图2,已知
,当
沿
平移到某一个位置时,四边形
为菱形,求此时
的长;
【拓展探究】
(3)如图3,连接
,若四边形
为菱形,且
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
【基础巩固】
(1)求证:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
【操作思考】
(2)如图2,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ded3fed7f7c6d4183b12ad97f5d625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
【拓展探究】
(3)如图3,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024dc2ccbbe321774df5d44e8785b203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
您最近一年使用:0次
真题
名校
3 . 如图①,小红在学习了三角形相关知识后,对等腰直角三角形进行了探究,在等腰直角三角形
中,
,过点
作射线
,垂足为
,点
在
上.
如图②,若点
在线段
上,画出射线
,并将射线
绕点
逆时针旋转
与
交于点
,根据题意在图中画出图形,图中
的度数为_______度;
(2)【问题探究】
根据(1)所画图形,探究线段
与
的数量关系,并说明理由;
(3)【拓展延伸】
如图③,若点
在射线
上移动,将射线
绕点
逆时针旋转
与
交于点
,探究线段
之间的数量关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38c15bc630ffe0f4d8d381dd13c4335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b455b110a30c1533d0a0657e0e48ac33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
如图②,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c15b72320563d6a10e05695cf26469c.png)
(2)【问题探究】
根据(1)所画图形,探究线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
(3)【拓展延伸】
如图③,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcec07f1a6bc0948d5406fd9e8200f2.png)
您最近一年使用:0次
2023-07-01更新
|
2151次组卷
|
13卷引用:专题10圆周角(4个知识点6种题型3种中考考法)-【帮课堂】2023-2024学年九年级数学上册同步学与练(苏科版)
(已下线)专题10圆周角(4个知识点6种题型3种中考考法)-【帮课堂】2023-2024学年九年级数学上册同步学与练(苏科版)2023年贵州省中考数学真题 (已下线)专题31图形的旋转(优选真题60道)-学易金卷:三年(2021-2023)中考数学真题分项汇编【全国通用】(已下线)2023年贵州省中考数学真题变式题22-25题河南省濮阳市清丰县2023-2024学年九年级上学期期中数学试题广东省深圳市龙岗区2023-2024学年八年级上学期期中数学试题(已下线)专题31 几何综合压轴题(共23道)-学易金卷:2023年中考数学真题分项汇编(全国通用)山东省临沂市罗庄区2023-2024学年九年级上学期期中数学试题湖北省省直辖县级行政单位天门市九校联考2023-2024学年九年级上学期月考数学试题广西南宁市邕宁区民族中学2023-2024学年九年级上学期10月月考数学试题陕西省西安市雁塔区陕西师范大学附属中学2023-2024学年八年级上学期期末数学试题(已下线)第5讲 探究题2024年河南省漯河市舞阳县中考导向总复习(一)数学试题
名校
4 . (1)【探究发现】如图①,已知矩形
的对角线
的垂直平分线与边
,
分别交于点E,F.求证:四边形
是菱形;
分别交矩形
的边
,
于点E,F,将矩形
沿
翻折,使点C的对称点与点A重合,点D的对称点为
,若
,
,求四边形
的周长;
(3)【拓展延伸】如图③,直线
分别交平行四边形
的边
,
于点E,F,将平行四边形
沿
翻折,使点C的对称点与点A重合,点D的对称点为
,若
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9766e5eb6796dafc5ffe212afdfc43c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
(3)【拓展延伸】如图③,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b173ac8cc4ac4f1c9e1daaa605fbb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2024-04-05更新
|
686次组卷
|
22卷引用:江苏省南通市海安市西片联盟2022-2023学年八年级下学期期中数学试题
江苏省南通市海安市西片联盟2022-2023学年八年级下学期期中数学试题江苏省南通市如东县2023-2024学年八年级下学期期中数学试题湖北省襄阳市枣阳市2021-2022学年八年级下学期期末数学试题2023年山东省青岛第二十六中学中考二模数学试题(已下线)八年级下学期数学期末质量检测B卷(测试范围:八下全部内容)-【单元测试】2022-2023学年八年级数学下册分层训练AB卷(人教版)湖北省利川市五校教联体2022-2023学年八年级下学期期中数学试题湖北省黄石市四区2022--2023学年八年级下学期期末数学试题(已下线)2023年青岛二模(探究拓展题)湖北省武汉市湖北大学附属中学2023-2024 学年九年级上学期月考数学试题湖北建始县官店镇民族中学2023-2024学年九年级上学期月考数学试题广东省佛山市三水区西南中学2023-2024学年九年级上学期第一次月考数学试题2023年四川省绵阳市涪城区中考模拟预测九年级数学模拟预测题甘肃省武威市武威第十中学2023-2024学年九年级下学期第一次月考数学试题(已下线)专题17八年级期中压轴题精选-【好题汇编】备战2023-2024学年八年级数学下学期期中真题分类汇编(人教版,湖北专用)江西省南昌市一中教育集团2023-2024学年八年级下学期期中数学试题(已下线)名校期中好题汇编(人教版八年级数学下册):专题四——特殊平行四边形(已下线)考前特训03 几何解答题探究综合压轴题-2024年中考数学二轮热点题型归纳与变式演练(全国通用)2023年四川省绵阳市涪城区中考数学终极模拟预测题(6月份)广东省江门市福泉奥林匹克学校2023-2024学年八年级下学期期中数学试题(已下线)专题06四边形折叠问题与最值问题(优选33道)-【好题汇编】备战2023-2024学年八年级数学下学期期末真题分类汇编(湖北专用)(已下线)专题05特殊的平行四边形(六大题型优选50道)-【好题汇编】备战2023-2024学年八年级数学下学期期末真题分类汇编(湖北专用)(已下线)2023—2024学年名校期末好题汇编(人教版八年级数学下册)——专题四—特殊的平行四边形
5 . 通过以前的学习,我们知道:“如图1,在正方形
中,
,则
”.
某数学兴趣小组在完成了以上学习后,决定对该问题进一步探究:
中,点
分别在线段
上,且
,试猜想
_________;
(2)【知识迁移】如图3,在矩形
中,
,点
分别在线段
上,且
,试猜想
的值,并证明你的猜想;
(3)【拓展应用】如图4,在四边形
中,
,点
分别在线段
上,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50718815e5b60540035d988ca80c0d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de32b9f279d0cbf3bc8ab9ada1f56111.png)
某数学兴趣小组在完成了以上学习后,决定对该问题进一步探究:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418611b495c71cbdc2f9102bcdc72300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ed2e6490abf519cf95cc1c4cb5ed60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94fef6d03173baf154ac97154571366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7996d44acc430748b604e121fee1cb8e.png)
(2)【知识迁移】如图3,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f7a5ed625693741921fa9148a6b74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418611b495c71cbdc2f9102bcdc72300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ed2e6490abf519cf95cc1c4cb5ed60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94fef6d03173baf154ac97154571366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885a273360456694a3d40a913f3df2fc.png)
(3)【拓展应用】如图4,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be012ed58284cbf788365899d13060c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a460f95e8ebabac97d572fecea8fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c18645bedb8cdf66c41ca9b0bf705f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6456423140d43ee212a5cc99fa6284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea624cb140001a7e9d7567903a29521.png)
您最近一年使用:0次
2024-03-17更新
|
136次组卷
|
9卷引用:江苏省宿迁市沭阳如东实验学校2023-2024学年九年级上学期第二次阶段检测数学试题
名校
6 . (1)观察推理:如图①,
中,
,直线l过点C,点A、B在直线l同侧,
,垂足分别为D、E.求证:
;
(2)类比探究:如图②,
中,
,将斜边
绕点A逆时针旋转
至
,连接
,求
的面积.
(3)拓展提升:如图③,等边
中,
,点O在
上,且
,动点P从点E沿射线
以
速度运动,连结
,将线段
绕点O逆时针旋转
得到线段
.要使点F恰好落在射线
上,求点P运动的时间t.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149d217efaf5090696904003ec06393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb394b62f512d43341cb42879973a1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c129fbab6979fd83f4c1ef52feb35557.png)
(2)类比探究:如图②,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178d4a866c3256aa4ba2d4a0c82b4ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020ebe1219437129358b986eb9e70bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f6bf45ecba77a2581e1142bd16bf8a.png)
(3)拓展提升:如图③,等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6818a98204f62c1b16699d26ca0c3f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be25dd5a289b24fa89d9939ef0ff864f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6485afddd0b6fe46abc1d0a3268b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9174c3b1324cf81098e42e0480bcc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
您最近一年使用:0次
2023-11-02更新
|
73次组卷
|
5卷引用:江苏省 镇江市丹阳市第八中学2023-2024学年八年级上学期第一次月考数学试题
解题方法
7 . 实践与探究
操作一:如图①,将矩形纸片
对折并展开,折痕
与对角线
交于点
,连接
,则
与
的数量关系为______.
操作二:如图②,摆放矩形纸片
与矩形纸片
,使
、
、
三点在一条直线上,
在边
上,连接
,
为
的中点,连接
、
.求证:
.
拓展延伸:如图③,摆放正方形纸片
与正方形纸片
,使点
在边
上,连接
,
为
的中点,连接
、
、
.已知正方形纸片
的边长为5,正方形纸片
的边长为
,求
的面积.
操作一:如图①,将矩形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/60ef95894ceebaf236170e8832dcf7e3.png)
操作二:如图②,摆放矩形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a8586ae37f043ee8d5162dec22126b.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fab40f323d2963eb0c4cdf39018fef.png)
拓展延伸:如图③,摆放正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a8586ae37f043ee8d5162dec22126b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a8586ae37f043ee8d5162dec22126b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9825e881728e22d0b8d4dab50854c433.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/5fa623b6-00f8-4955-ad03-22b863675f25.png?resizew=510)
您最近一年使用:0次
2023-04-26更新
|
386次组卷
|
6卷引用:江苏省淮安市淮安区2022-2023学年八年级下学期期末调研测试数学试题
江苏省淮安市淮安区2022-2023学年八年级下学期期末调研测试数学试题2023年山东省菏泽市郓城县九年级下学期第一次模拟数学考试 2023年山东省菏泽市郓城县中考一模数学试题(已下线)专题16 几何综合压轴-学易金卷:2023年中考数学一模试题分项汇编(山东专用)(已下线)第5章 特殊平行四边形 章末重难点检测卷-【帮课堂】2022-2023学年八年级数学下册同步精品讲义(浙教版)(已下线)2023年广东省佛山市中考一模数学试卷变式题21-23题
名校
8 . 问题情境:苏科版八年级下册数学教材第94页第19题第(1)题是这样一个问题:
如图1,在正方形
中,点
分别在边
上,且
,垂足为M.那么
与
相等吗?
___________
(填“
”或“
”);
在“问题情境”的基础上,继续探索:
问题探究:
(2)如图2,在正方形
中,点
分别在边
和
上,且
,垂足为M.那么
与
相等吗?证明你的结论;
问题拓展:
(3)如图3,在(2)的条件下,当
在正方形
的对角线
上时,连接
,将
沿着
翻折,点
落在点
处.
①四边形
是正方形吗?请说明理由;
②若
,如图4,点
在
上,且
,直接写出
的最小值为__________.
如图1,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20cb2c77ea29b6eabbc477bc3743859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e22ba3e6e1c1d6b12d9b8baa8d1f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411837b4b3078d05b43cb0439259a362.png)
在“问题情境”的基础上,继续探索:
问题探究:
(2)如图2,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6241f9ef86cd0a902cbadaf336767dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20cb2c77ea29b6eabbc477bc3743859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de97dfb4a50e1e852ac0d09c3605d1ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3956f008cc29ca4bae44a087d5427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
问题拓展:
(3)如图3,在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234cdeeee94033501fca6596894f7b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
①四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79549dd9d678012702fb1b6a2d8e546.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c1110da9c8e44e66479ecadda71cbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b952873c9da174d3671caf4541e3a1.png)
您最近一年使用:0次
2023-08-18更新
|
414次组卷
|
6卷引用:江苏省淮安市洪泽区2022-2023学年八年级下学期期末数学试题
江苏省淮安市洪泽区2022-2023学年八年级下学期期末数学试题江苏省淮安市金湖县2022-2023学年八年级下学期期末数学试题江苏省淮安市洪泽区、金湖县2022-2023学年八年级下学期期末数学试题江苏省宜兴市树人中学教育集团2023-2024学年八年级下学期3月月考数学试题(已下线)专题01 平行四边形(5种模型与解题方法)-【帮课堂】2023-2024学年八年级数学下册同步学与练(苏科版)(已下线)(期中期末真题汇编)第12章 全等三角形(分层精练)-【题型分类精粹】2023-2024学年八年级数学上学期期中期末复习讲练系列【考点闯关】(人教版)
真题
名校
9 . 矩形ABCD中,
=
(k>1),点E是边BC的中点,连接AE,过点E作AE的垂线EF,与矩形的外角平分线CF交于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/18/bcddbed5-6677-42a7-9b9f-67aaf5322d4b.png?resizew=639)
(1)【特例证明】如图(1),当k=2时,求证:AE=EF;
小明不完整的证明过程如下,请你帮他补充完整.
(2)【类比探究】如图(2),当k≠2时,求
的值(用含k的式子表示);
(3)【拓展运用】如图(3),当k=3时,P为边CD上一点,连接AP,PF,∠PAE=45°,
,求BC的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2465ee1fec12351943f15055dfd6ec73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4645b6368eae25e9ecede56e45a8459.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/18/bcddbed5-6677-42a7-9b9f-67aaf5322d4b.png?resizew=639)
(1)【特例证明】如图(1),当k=2时,求证:AE=EF;
小明不完整的证明过程如下,请你帮他补充完整.
证明:如图,在BA上截取BH=BE,连接EH.![]() ∵k=2, ∴AB=BC. ∵∠B=90°,BH=BE, ∴∠1=∠2=45°, ∴∠AHE=180°-∠1=135°. ∵CF平分∠DCG,∠DCG=90°, ∴∠3= ![]() ∴∠ECF=∠3+∠4=135°. ∴…… (只需在答题卡对应区域写出剩余证明过程) |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114a2e56d9a32e3886fd517a85ede50d.png)
(3)【拓展运用】如图(3),当k=3时,P为边CD上一点,连接AP,PF,∠PAE=45°,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3864fbf8f38f0285c22abbd5e31f8d15.png)
您最近一年使用:0次
2022-09-01更新
|
2072次组卷
|
12卷引用:黄金卷01-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷(江苏南通专用)
(已下线)黄金卷01-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷(江苏南通专用)2022年湖北省襄阳市中考数学真题广东省深圳市福田外国语学校2022-2023学年九年级上学期第一次质检数学试卷广西壮族自治区南宁市西乡塘区广西大学附属中学2022-2023学年九年级上学期第三次月考数学试题(已下线)第27章相似01讲核心(已下线)黄金卷3-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷(陕西专用)2023年河南省安阳市滑县中考二模数学试题(已下线)2023年湖北省中考数学真题变式题21-24题(已下线)2023年河南省二模(几何综合1)江西省吉安市吉安县城北中学2023-2024学年九年级上学期月考数学试题(已下线)第5讲 探究题2023年贵州省黔东南十八校中考联考数学模拟预测题(一)
真题
10 . 【问题背景】
人教版八年级下册数学教材第63页“实验与探究”问题1如下:如图,正方形
的对角线相交于点
,点
又是正方形
的一个顶点,而且这两个正方形的边长相等,无论正方形
绕点
怎样转动,两个正方形重叠部分的面积,总等于一个正方形面积的
.想一想,这是为什么?(此问题不需要作答)
九年级数学兴趣小组对上面的问题又进行了拓展探究、内容如下:正方形
的对角线相交于点
,点
落在线段
上,
(
为常数).
(1)如图1,将
的直角顶点
与点
重合,两直角边分别与边
,
相交于点
,
.
①填空:
______;
②求证:
.(提示:借鉴解决【问题背景】的思路和方法,可直接证明
;也可过点
分别作
,
的垂线构造全等三角形证明.请选择其中一种方法解答问题②.)
【类比探究】
(2)如图2,将图1中的
沿
方向平移,判断
与
的数量关系(用含
的式子表示),并说明理由.
【拓展运用】
(3)如图3,点
在边
上,
,延长
交边
于点
,若
,求
的值.
人教版八年级下册数学教材第63页“实验与探究”问题1如下:如图,正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e2699bbd62cf03b5f1eaae984287d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e2699bbd62cf03b5f1eaae984287d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
九年级数学兴趣小组对上面的问题又进行了拓展探究、内容如下:正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52f125abf9625888d5feb7d6d2b5fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)如图1,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d244880e9a28a02df25b4e864b28975e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
①填空:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acd79bb9fb06f7c806eb6e17e4b613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3304c41b7ef6d6f43ec3090c5362f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
【类比探究】
(2)如图2,将图1中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
【拓展运用】
(3)如图3,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f27564bb46555b27e130fe9aad7615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](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/9f3d9105c0a55832a1ba674ec12364b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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