1 . 李老师善于通过合适的主题整合教学内容,帮助同学们用整体的、联系的、发展的眼光看问题,形成科学的思维习惯,下面是李老师在“利用角的对称性构造全等模型”主题下设计的问题,请你解答.
①如图1,
是
的角平分线,
,在
上截取
,连接
,则
与
的数量关系是__________;
②如图2,
的角平分线
、
相交于点P.当
时,线段
与
的数量关系是__________;
(2)【探究迁移】
如图3,在四边形
中,
,
的平分线与
的平分线恰好交于
边上的点P,试判断
与
的数量关系,并说明理由.
(3)【拓展应用】在(2)的条件下,若
,当
有一个内角是
时,直接写出边
的长.
①如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc2f5f6d9efe3852a2329ea927abcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8bc2b99ffb78e8b6ca21fccdbe2906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
②如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/998329f9cdb86f5d60d7d5d70fc3781e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
(2)【探究迁移】
如图3,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609ada36dd56b33279103ebc1f90bbac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(3)【拓展应用】在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df56c9e080e718e2c0f2361a18f5498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e78042a384255038de485fd7bc0839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
真题
名校
2 . 【问题呈现】
和
都是直角三角形,
,连接
,
,探究
,
的位置关系.
时,直接写出
,
的位置关系:____________;
(2)如图2,当
时,(1)中的结论是否成立?若成立,给出证明;若不成立,说明理由.
【拓展应用】
(3)当
时,将
绕点C旋转,使
三点恰好在同一直线上,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41663d9e5e18891475aeaa98794f33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5efe95decdbbc144754cda971f62f2.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://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
【拓展应用】
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd82901e18614746fffc40f8de8e230e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4817f6d025306bfcba653b4e8d4dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
2023-06-22更新
|
2125次组卷
|
28卷引用:河南省周口市淮阳区2023-2024学年九年级上学期12月月考数学试题
河南省周口市淮阳区2023-2024学年九年级上学期12月月考数学试题河南省漯河市临颍县2023-2024学年九年级上学期期末数学试题河南省新乡市辉县市2023-2024学年九年级上学期期末数学试题河南省鹤壁市浚县实验初级中学2023-2024学年九年级上学期11月月考数学试题2024年河南省汝南县中考一模数学模拟试题2023年湖北省黄冈市中考数学真题(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】辽宁省鞍山市千山区实验教育集团2023-2024学年九年级上学期10月月考数学试题(已下线)2023年湖北省黄冈市中考数学真题变式题21-24题山东省济南市平阴县教育教学研究中心2023-2024学年九年级上学期期中数学试题(已下线)专题4.46 相似三角形几何模型(旋转模型)(培优练)-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)江苏省泰州市海陵区民兴中英文学校2023-2024学年九年级上学期12月月考数学试题江苏省苏州市2023-2024学年九年级上学期期末数学试题山东省济南市平阴县2023-2024学年九年级上学期期中数学试题(已下线)专题2 迁移信息黑龙江省哈尔滨市香坊区第三十九中学2023-2024学年九年级下学期开学测数学(五四制)试题山东省济南市商河县清华园学校2023-2024学年上学期九年级月考数学测试题浙江省金华市兰溪市第八中学2023-2024学年上学期学习能力调查(一)九年级数学试题湖北省十堰市郧西县2023-2024学年九年级下学期期中数学试题江苏省南通市如皋市石庄镇初级中学2023-2024学年九年级下学期第一次阶段性数学试题2024年中考数学模拟预测题五2024年山东省威海市经济技术开发区皇冠中学中考一模数学模拟试题2024年湖北省丹江口市中考二模数学试题2024年湖北省十堰市竹山县中考模拟数学试题(已下线)专题10 三角形压轴题综合-2024年中考数学二轮热点题型归纳与变式演练(全国通用)湖北省黄石市阳新县陶港镇初级中学2023-2024学年九年级下学期期中数学试题2024年山东省济南市商河县中考二模数学试题2024年四川省乐山实验中学中考数学一调试题
3 . 如图,
是等腰三角形,
.点D在直线
上,连接
,将线段
绕点D逆时针旋转
得到
,连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d9cd3bf4f39c2837349fe1f8ab7428.png)
如图1,若
__________,
与
的数量关系是___________________.
(2)类比探究:
如图2,若
,(1)中的两个结论是否仍然成立?若成立,请说明理由;若不成立,请写出新的结论,并说明理由.
(3)拓展应用:
若
,过点E作
于点F,
,请直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3c7a4c1b3fd2eb68098f9e0107c172.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d9cd3bf4f39c2837349fe1f8ab7428.png)
如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60e9c55329e5856b886aac3af3987b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
(2)类比探究:
如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac762a2899a58faa0d3ab44f1281fa.png)
(3)拓展应用:
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8493fee0c66e9b515900c9da23eefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68004768b879c6a052f45a2c45217cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
您最近一年使用:0次
2024-05-22更新
|
137次组卷
|
2卷引用:2024年河南省南阳市新野县中考二模数学试题
4 . 人教版教材中的折纸活动,引起了许多同学的兴趣.在折纸的过程中,同学们不仅发展了空间观念,还积累了数学活动经验.
【操作】在矩形
中,
,点E在边
上,连接
,将
沿
折叠,点B的对应点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/ee910c41-67f7-4ef8-a48b-771ab555901d.png?resizew=353)
【发现】
(1)如图1,若点M,
,E在同一条直线上,求证:
为等腰三角形;
【探究】
(2)若点落在矩形对角线上,求
的长;
【拓展】
(3)如图2,过点
作
,当
面积最大时,请直接写出
的长.
【操作】在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc5840a6d28b6eeb4caed7d5e11ffd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6818a98204f62c1b16699d26ca0c3f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/ee910c41-67f7-4ef8-a48b-771ab555901d.png?resizew=353)
【发现】
(1)如图1,若点M,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b100429009a720f571a31c3a23d6ba.png)
【探究】
(2)若点落在矩形对角线上,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
【拓展】
(3)如图2,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7d034584d26c57b85067af05b30aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7395b0abf90241e101e6528a655973f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
2023-06-19更新
|
108次组卷
|
4卷引用:2023年河南省漯河市召陵区中考二模数学试题
2023年河南省漯河市召陵区中考二模数学试题(已下线)2023年河南省二模(几何综合2)2023年河南省南阳市唐河县四校联考中考模拟数学模拟试题(二)(已下线)第03讲 相似三角形-【帮课堂】2023-2024学年九年级数学上册同步学与练(浙教版)
5 . 综合与实践课上,老师带领同学们开展以“图形的变化”为主题的数学活动.
(1)观察发现
如图1,如图1,将平面直角坐标系中
进行平移后得到
,则线段
与线段
的位置关系为 ,数量关系为 ;
如图2,将平面直角坐标系中
以点B为旋转中心逆时针旋转
得到
则线段
所在直线与线段
所在直线的位置关系为 ;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/2/8f6d0128-4f71-47f3-ba0b-61767ee1f81c.png?resizew=368)
(2)探究迁移
如图3,将平面直角坐标系中
进行平移后得到
,再将
以点
为旋转中心逆时针旋转
得到
线段
所在直线与线段
所在直线相交于点P,锐角
记为β,请判断α和β的数量关系并说明理由;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/2/4f2cddfd-d0b4-4bb5-bb19-f9043e407dec.png?resizew=384)
(3)拓展应用
如图4,平面直角坐标系中
,
,
,
,将
在x轴上水平平移得到
平移后以
为旋转中心将
逆时针旋转
得到
线段
所在直线与线段
所在直线在P点相交,若点
在某个位置可使点P与点
或点
重合,请直接写出m的值.
(1)观察发现
如图1,如图1,将平面直角坐标系中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e968a680c085015f5bfea60f7db9850f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b11ec71350bc49e9b73959baedcad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/2/8f6d0128-4f71-47f3-ba0b-61767ee1f81c.png?resizew=368)
(2)探究迁移
如图3,将平面直角坐标系中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b40aa8d2482d698ebef69cf225f99f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740f166d28ee1b09cde0c4e6420f080c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d77f02e8eb6827be9c42cdd153ccddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1369e52c1f7a1df05b7da4c7ad310541.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/2/4f2cddfd-d0b4-4bb5-bb19-f9043e407dec.png?resizew=384)
(3)拓展应用
如图4,平面直角坐标系中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c513dca3b8c31bc8d0ed4301e94cc1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f304c4bfe683ced57419593537402d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602acab78bfc4aa216e8ace528efff66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cca121a2e8b03262a1e8b2508f1c6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6012e5f062202e67356fd8d678fbd5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fd651dd5027d57d542ab510f8a9ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f68dfc2ca5a280a7439b8769188816f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d77f02e8eb6827be9c42cdd153ccddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc43bee5e0ef79167751b587ecbe809e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
名校
6 . 由两个顶角相等且有公共顶角顶点的特殊多边形组成的图形,如果把它们的底角顶点连接起来,则在相对位置变化的过程中,始终存在一对全等三角形,我们把这种模型称为“手拉手模型”.
如图1所示,两个等腰直角三角形
和
中,
,
,
,连接
、
,两线交于点P,
和
的数量关系是 ;
和
的位置关系是 ;
(2)【类比探究】
如图2所示,点P是线段
上的动点,分别以
、
为边在
的同侧作正方形
与正方形
,连接
分别交线段
、
于点M、N.
①求
的度数;
②连接
交
于点H,直接写出
的值;
(3)【拓展延伸】
如图3所示,已知点C为线段
上一点,
,
和
为
同侧的两个等边三角形,连接
交
于N,连接
交
于M,连接
,直接写出线段
的最大值.
如图1所示,两个等腰直角三角形
![](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/e30e50e094cd2849e38859b36aad0b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26813466e2ee49a493881a4384fc8748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)【类比探究】
如图2所示,点P是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bdc60a42a1addaf772c18972e576fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc497d9e08a3652fccce2674b5e1bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c98538f59b61d4e4ec92f8aa54bf0d.png)
②连接
![](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/ef9c29abd53456f9beb7bc56273e85bb.png)
(3)【拓展延伸】
如图3所示,已知点C为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb6823a329628699619a39cde927510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2023-05-24更新
|
741次组卷
|
4卷引用:2023年河南省郑州市第八中学中考二模数学试题
名校
7 . 【问题背景】:
如图1,在
中,
,
,
,点
是斜边
的中点,过点
作
交
于点
.
【实验探究】:
(1)数学活动课中,小明同学将图1中的
绕点
按顺时针方向旋转
,如图2所示,得到结论:①
______;②直线
与
所夹锐角的度数为______;
(2)若我们继续将
绕点
按顺时针方向旋转,旋转至如图3所示位置.请问探究(1)中的结论是否仍然成立?并说明理由.
【拓展延伸】:
(3)在以上探究中,当
旋转至
、
、
三点共线时,则
的面积为______.
如图1,在
![](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/f7bae5203f4b4acf23779114b3466e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab926d89b65f26c12e3da73ef1e5cf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/7f8daff96303a07819bd4ee47731e73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
【实验探究】:
(1)数学活动课中,小明同学将图1中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d698ee39cd00a9b6384e0c4897a055a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)若我们继续将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
【拓展延伸】:
(3)在以上探究中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/45251b23-026d-452a-99d7-ada495573171.png?resizew=433)
您最近一年使用:0次
2023-03-06更新
|
229次组卷
|
4卷引用:河南省郑州市外国语中学2022-2023学年九年级下学期入学测试数学试题
河南省郑州市外国语中学2022-2023学年九年级下学期入学测试数学试题2024年河南省洛阳市东升第二初级中学第一次模拟考试数学试题(已下线)2023年湖北省黄冈市中考二模数学试题变式题21-24题福建省莆田市城厢区擢英中学2023-2024学年九年级上学期期中数学试题
8 . 【问题背景】
“综合与实践”课上,王老师带领同学们剪拼图形,用发展的眼光看问题,感受图形的变换美!
【特例感知】
(1)如图(1),纸片
为矩形,且
,
,点E,F分别为边
,
的中点,沿
将纸片剪成两部分,将纸片
沿纸片
的对角线
方向向上平移.
①当纸片
平移至点
与
的中点O重合时,两个纸片重叠部分
的面积与原矩形纸片
的面积之比是______.
②当两个纸片重叠部分
的面积与原矩形纸片
的面积之比是
时,则平移距离
为______.
【类比探究】
(2)如图(2),当纸片
为菱形,
,
时,将纸片
沿其对角线
剪开,将纸片
沿
方向向上平移.当两个纸片重叠部分
的面积与纸片
的面积之比为
时,求平移距离
(用含a的式子表示).
【拓展延伸】
(3)某小组将图(2)剪下来的
与图(1)中的四边形
按图(3)的方式放在同一平面内,使点L与点B重合,
与
重合.将
从如图(3)所示的起始位置开始绕B点逆时针旋转
,旋转过程中,边
与边
相交于点T,边
与边
相交于点S,连接
.请直接写出旋转过程中
,
,
之间的数量关系.
“综合与实践”课上,王老师带领同学们剪拼图形,用发展的眼光看问题,感受图形的变换美!
【特例感知】
(1)如图(1),纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac943d8c2eb91c0082ada87857d1ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fa3aea72ccc36948a4a90f7368f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94c5119a5d7197604b58e8025ca5ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6d456e2adab93eabc931b3227bb79f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21002725043bdace95b3244d4c75dd74.png)
①当纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94c5119a5d7197604b58e8025ca5ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21002725043bdace95b3244d4c75dd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0761f984b8c8cb494c69ede2877804ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
②当两个纸片重叠部分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0761f984b8c8cb494c69ede2877804ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8d1ca7682da10dc7f36e858593d51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827be85b8f921007a5cf9edb64bd3491.png)
【类比探究】
(2)如图(2),当纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72111572d7898e53fddf7a8cd49c510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d896cfc194941ef748be924df040dd5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772441094bf51a2c815c9f3a1d625730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72111572d7898e53fddf7a8cd49c510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990f13b38111f7195b356cc72287f690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b90fc2d3503ca51568a92374ae7f022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990f13b38111f7195b356cc72287f690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb72f5d18aa205904fffc46a8ec3f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b90fc2d3503ca51568a92374ae7f022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8236dc949c9138b6b01c9093b678ae.png)
【拓展延伸】
(3)某小组将图(2)剪下来的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140bca725eb48e1d187a79372f1691f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6d456e2adab93eabc931b3227bb79f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f83c8c210a7e00e1594b7857dc96a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140bca725eb48e1d187a79372f1691f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f895ec9007b1dabc9d9dec9a307ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78324fc0f0ebc4e36e5a5af16483483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f83c8c210a7e00e1594b7857dc96a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4bab74b21722ce5f1d44a6e1de32b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0216422054380bcbd2dcbc38aac8ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6664180a5a14191295b419be0adb087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedc13a4c111aff86bf3485b239d9096.png)
您最近一年使用:0次
9 . 问题情境:
在数学课上,张老师带领学生以“图形的平移”为主题进行教学活动.在菱形纸片
中,
,对角线
,将菱形沿对角线
剪开,得到
和
.将
沿射线
方向平移一定的距离,得到
.
观察发现:
(1)如图①,菱形
中,
;
如图②,连接
,四边形
的形状是 ;
(2)将
沿直线
翻折,得
,如图③,然后沿射线
方向进行平移,连接
,若添加一个条件,能否使得四边形
是一个特殊的四边形?若能,请写出添加的条件和这个特殊的四边形,并写出证明过程,若不能,说明理由.
(3)在(2)的条件下,设
和
相交于点
,当
是
的三等分点时,直接写出
的面积.
在数学课上,张老师带领学生以“图形的平移”为主题进行教学活动.在菱形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71e6ea7333dbc78d0a7b9bc3892f940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73636989e83905f8800a865c2b608c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73636989e83905f8800a865c2b608c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
观察发现:
(1)如图①,菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629f896496e9a6fd7df6e0a56e0a6243.png)
如图②,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c30c0d64b256b3efc386ff6276f1ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f46b357e543eb2e895d0ea4742f4546.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da547af5752515964c58948ec3a5f89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08221bb58fef1459a6b6412497d187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f920913237cb68d097c13578691112f.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f574463a3c3541e3e42cf7e1fee8e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369c774635fb4384dcbabe732c7c5b27.png)
您最近一年使用:0次
2024-05-28更新
|
99次组卷
|
2卷引用:2024年河南省开封市中招第一次模拟考试数学试题
10 . 综合与实践
综合与实践课上,老师让同学们以“三角形与旋转”为主题开展数学活动.
【问题情景】如图,在
中,
是射线
上的一动点(不与点
重合),将线段
绕点
按顺时针方向旋转
得到
,连接
.
【问题探究】
(1)勤奋小组提出的问题:如图1,若
,则
之间的数量关系是______.
【类比延伸】
(2)智慧小组提出的问题:如图2,若
,探究
之间的数量关系.
【拓展探究】
(3)创新小组突发奇想,将问题迁移到平面直角坐标系中,如图3,若
,则在点
运动的过程中,当
时,请直接写出点
的坐标.
综合与实践课上,老师让同学们以“三角形与旋转”为主题开展数学活动.
【问题情景】如图,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8073465b2bfe822bc91d3b655fd3c923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd358585a317d08ef816ff357db49c8.png)
【问题探究】
(1)勤奋小组提出的问题:如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35733912d77e05487445e97b34fa52b3.png)
【类比延伸】
(2)智慧小组提出的问题:如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac762a2899a58faa0d3ab44f1281fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35733912d77e05487445e97b34fa52b3.png)
【拓展探究】
(3)创新小组突发奇想,将问题迁移到平面直角坐标系中,如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f40c2f0f89ad669e6fbfb5daafca83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9817d6eaf6f9454152b2891f33aaa760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2024-04-18更新
|
133次组卷
|
2卷引用:2024年河南省濮阳市南乐县中考一模数学模拟试题