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解题方法
1 . (1)问题
如图1,在四边形
中,点P为
上一点,当
时,求证:
.
(2)探究
若将
角改为锐角(如图2),其他条件不变,上述结论还成立吗?说明理由.
(3)应用
如图3,在
中,
,
,以点A为直角顶点作等腰
.点D在
上,点E在
上,点F在
上,且
,若
,求
的长.
如图1,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7502d2b89b731a7c11faa97815d46d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c4bc1c164e8dd6747cf998b237ef90.png)
(2)探究
若将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
(3)应用
如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7099026716ee1821dd7d9f157dc055f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e7ba6e267dde1a65a98f9f36b585ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02a4bbef957f179f55c28b37c64ce37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4307209e1e5cad88fc1b8163858688ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/b1005612-29bc-4caf-9915-c0cc0f88f83a.png?resizew=484)
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20卷引用:贵州省毕节市织金县2023-2024学年九年级上学期期末数学试题
贵州省毕节市织金县2023-2024学年九年级上学期期末数学试题山东省济南市济阳区2021-2022学年九年级上学期期中考试数学试题2022年山东省泰安市岱岳区中考三模数学试题2022年山东省菏泽市中考第三次模拟考试数学试题2022年山东省菏泽市牡丹区九年级中考三模数学试题四川省内江市隆昌市第一中学2022-2023学年九年级上学期第三次月考数学试题山东省济南市平阴县2022-2023学年九年级上学期期末数学试题(已下线)第14讲 相似三角形中的“一线三等角”模型-【多题一解&一题多解】冲刺2023年中考数学满分应对方法与策略(全国通用)山东省泰安市东平县2022-2023学年八年级下学期期末数学试题广东省深圳市南山区哈尔滨工业大学(深圳)实验学校2023-2024学年九年级上学期期中数学试题安徽省合肥市2023-2024学年九年级上学期期中模拟数学试题安徽省宿州市萧县2023-2024学年九年级上学期期中数学试题河南省南阳市唐河县2023-2024学年九年级上学期期中数学试题广东省佛山市南海外国语学校2023-2024学年九年级上学期第三次月考数学试题(已下线)清单18 相似三角形的10大经典模型-2023-2024学年九年级数学上学期期末考点大串讲(苏科版)山东省济南市历城区2023-2024学年九年级上学期期末数学试题浙江省宁波市2023-2024学年九年级上学期期末考试数学试题广东省河源市和平县2023-2024学年九年级上学期期末数学试题四川省遂宁市蓬溪县蓬溪中学校2023-2024学年九年级上学期期中数学试题四川省内江市隆昌市知行中学2023-2024学年九年级上学期第三次月月考数学试题
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2 . 背景:一次小组合作探究课上,小明将两个正方形按如图1所示的位置摆放(点E、A、D在同一条直线上),小组讨论后,提出了下列三个问题,请你帮助解答:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/318e55d4-f455-48db-9d82-f3ea81bfb7a0.png?resizew=465)
(1)如图2,将正方形
绕点A按逆时针方向旋转,求
与
的数量关系和位置关系;
(2)如图3,把背景中的正方形分别改写成矩形
和矩形
,且
,
,
,将矩形
绕点A按顺时针方向旋转,求
与
的数量关系和位置关系;
(3)在(2)的条件下,小组发现:在旋转过程中,
的值是定值,请求出这个定值.(直接写出答案)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/318e55d4-f455-48db-9d82-f3ea81bfb7a0.png?resizew=465)
(1)如图2,将正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
(2)如图3,把背景中的正方形分别改写成矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9213da82fd4080bb3097671bdd2a28e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070bc896d35495237fd65576e9b6f88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
(3)在(2)的条件下,小组发现:在旋转过程中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd35e8ebeb27cf3a4128c0c59904e63.png)
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12卷引用:贵州省贵阳市修文县2022-2023学年九年级上学期期末数学试题
贵州省贵阳市修文县2022-2023学年九年级上学期期末数学试题2021年河南师范大学附属中学中考名校内部摸底数学试题2021年河南省河南师范大学附属中学九年级下学期第二次模拟考试数学试题(已下线)数学-(河南卷)【试题猜想】2021年中考考前最后一卷2021年湖北省襄阳市襄州区中考数学适应性试题(已下线)专题4.24 相似三角形的性质(知识讲解)-2022-2023学年九年级数学上册基础知识专项讲练(北师大版)河南省开封市东北学区2021-2022学年九年级上学期期中数学试题(已下线)专题27.19 相似三角形的性质(知识讲解)-2022-2023学年九年级数学下册基础知识专项讲练(人教版)(已下线)专题6.20 相似三角形的性质(知识讲解)-2022-2023学年九年级数学下册基础知识专项讲练(苏科版)河南省驻马店市正阳县2022-2023学年九年级上学期期末数学试题福建省宁德蕉城校际联考2022-2023学年九年级上学期期中数学试题(已下线)专题4.53 相似三角形的性质与判定综合专题(分层练习)(综合练)-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)
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3 . 根据以下素材,探索完成任务.
运用二次函数来研究植物幼苗叶片的生长状况 | ||
素 材 | 在大自然里,有很多数学的奥秘.一片美丽的心形叶片、一棵生长的幼苗都可以看作把一条抛物线的一部分沿直线折叠而形成. | |
问题解决 | ||
任 务 1 | 确定心形叶片的形状 | 如图3建立平面直角坐标系,心形叶片下部轮廓线可以看作是二次函数![]() |
任 务 2 | 研究心形叶片的尺寸 | 如图3,心形叶片的对称轴直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
任 务 3 | 探究幼苗叶片的生长 | 小李同学在观察幼苗生长的过程中,发现幼苗叶片下方轮廓线都可以看作是二次函数![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-05-04更新
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1046次组卷
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11卷引用:2023年贵州省贵阳市观山湖区中考模拟数学模拟预测题
2023年贵州省贵阳市观山湖区中考模拟数学模拟预测题2023年贵州省铜仁市第五中学中考数学四模模拟预测题2023学年贵州省铜仁市第五中学九年级下学期第四次模拟数学模拟预测题2023年浙江省永康市中考一模数学试题2023年江苏省苏州市胥江实验中学校中考二模数学试题陕西省西安市高新二中2023-2024学年九年级上学期期末数学试题广东省深圳市南山区南山外国语学校(集团)2023-2024学年九年级下学期开学考数学试题2023年浙江省温州市育英国际实验学校娄桥校区中考模拟数学模拟预测题2023年浙江省温州市瓯海区育英国际实验学校娄桥校区中考数学模拟预测试题(已下线)重难点01 二次函数与几何的综合训练(9大题型+限时分层检测)-2024年中考数学【热点·重点·难点】专练(全国通用)2024年广东省深圳市南山区桃源中学中考三模数学试题
4 . 如图,四边形
是正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/9/1106efbd-6709-4bd8-bd28-17d0b98f07bb.png?resizew=386)
(1)问题解决:如图①,若
,
分别是
,
上的点,且
.求证:
;
(2)类比探究:如图②,若点
,
,
,
分别在
,
,
,
上,且
,求证:
F.
(3)迁移应用:如图③,在
中,
,
,点
是
的中点,点
是
上一点,且
,求
:
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/9/1106efbd-6709-4bd8-bd28-17d0b98f07bb.png?resizew=386)
(1)问题解决:如图①,若
![](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/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9576dc0787e3a65d7f8ea2a436617c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9327d1c2faee1d33db246ab52e43e4f9.png)
(2)类比探究:如图②,若点
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96461af9193d5d7867ddf8fcbefcaec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e336d8c1385e1a71ae67b7ee01db1d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23131e0a1dd1bf36c70eff2a54fe65e.png)
(3)迁移应用:如图③,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c7d01c3618d579121d95d41a63c565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c029f2663b3fd557c9169e295c353e8.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96dae1059483b2532096123ee80ee50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9171484a68c84cad91e4f2233392f600.png)
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5 . 小星和小红在学习了正方形的相关知识后,对正方形内一些特殊线段的关系进行探究.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/2363fdc9-945e-42bb-afcf-aadd95368e1e.png?resizew=429)
(1)问题解决
如图①,在正方形
中,E,F分别是
边上的点,连接
,且
,求证:
;
(2)类比探究
如图②,在正方形
中,E,F,G,H分别是
边上的点,连接
,且
,求证:
;
(3)迁移应用
如图③,在
中,
,
,D是
的中点,E是
边上的点,连接
,且
,求
的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/2363fdc9-945e-42bb-afcf-aadd95368e1e.png?resizew=429)
(1)问题解决
如图①,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ced324a15510f9cf7518d8c277c6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebf73d933dd233b8879764892b26c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e22ba3e6e1c1d6b12d9b8baa8d1f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9327d1c2faee1d33db246ab52e43e4f9.png)
(2)类比探究
如图②,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111eaab62c10ed8ec2c0963ac066062c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76b9b2f4987b713e347dc38050af3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de64cbea23ec8a57a4705d9f16297d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddeac29a796a890dac3c4cc58de07ac7.png)
(3)迁移应用
如图③,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/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0032f850bd19a3af6c44c416b0a2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c897a54f2e36bc4b52fba74b41c89d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991cf23efcc5f3b7b8c60bda5f9915b1.png)
您最近一年使用:0次
2023-02-24更新
|
412次组卷
|
4卷引用:贵州省贵阳市2022-2023学年九年级上学期期末数学试题
6 . 图形的探究中,常用三角形通过一些图形变换,将图形拼在一起,以探究其线段,角之间的关系,小李用两个三角形,
,
,
.开展如下的探究活动:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/d1611bcd-86dd-41db-a991-c8c7117d6dcf.png?resizew=621)
[探究1]如图1,两个三角形如图1摆放,点B在CD上时,求证:
;
[探究2]如图2,将
绕点C逆时针旋转旋转
,过点D作
交AB于点F.线段DF与AF有何数量关系?并说明理由;
[探究3]在探究2的条件下,若AB分别交CD于M,AB的延长线CE于点P(如图3),线段PM,PF,PA有何数量关系,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5adc18ca424552b35ab939e9d57943e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17101383eb0787edaaa35adfcd20d5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414dd77f2a63357f08fc8d61d611d69e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/d1611bcd-86dd-41db-a991-c8c7117d6dcf.png?resizew=621)
[探究1]如图1,两个三角形如图1摆放,点B在CD上时,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640454e33a4238c7d8e1c78bf6f099ca.png)
[探究2]如图2,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2598f844644c4245eb226ecca57ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974762e15695c9482f34a43ffe1c8585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ae39b21e756f6067892180b3772f10.png)
[探究3]在探究2的条件下,若AB分别交CD于M,AB的延长线CE于点P(如图3),线段PM,PF,PA有何数量关系,并加以证明.
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7 . 数学活动课上,张老师引导同学们进行如下探究,如图1,将长为
的铅笔
斜靠在垂直于水平桌面
的直尺
的边沿上,一端A固定在桌面上,图2是示意图.活动一:如图3,将铅笔
绕端点A顺时针旋转,
与
交于点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/43f32b00-acd6-4695-9e82-60b223a73eea.png?resizew=246)
(1)数学思考:若
垂直
,设
.
①
的长是______
(用含x的代数式表示),
的长是______
(用含y的代数式表示)
②求y与x的函数关系式.
(2)活动二:若(1)中的x,y满足
,根据(1)中求得的y与x的函数关系式,求x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689ff84e2d7f52c7446ef789a54557da.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/ecff6005f926665a926c07ad62e0f032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/43f32b00-acd6-4695-9e82-60b223a73eea.png?resizew=246)
(1)数学思考:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300939c07aa8b4cf92b8db94eb400fc0.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
②求y与x的函数关系式.
(2)活动二:若(1)中的x,y满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581f4963e80a21e9bb1dac9bb79263c4.png)
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8 . 综合与实践
【问题情境】
学习完旋转这章内容后,在一次数学活动课上,刘老师让学生用一张矩形纸片(矩形
)与一张直角三角形纸片(
)进行数学活动,如图1,
,
,
,点M是
和
的中点,将
绕点M顺时针旋转
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/20/c2dc787d-20fb-42be-b683-a24b34b9b629.png?resizew=155)
【探究发现】
(1)如图2,自强小组发现,在旋转过程中,当
时,四边形
是一个特殊的四边形.请你判断四边形
的形状,并说明理由;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/20/03ab91c4-770e-4954-850f-ef40a9509e13.png?resizew=154)
(2)奋进小组在自强小组的基础上连接
,通过探究发现,在旋转过程中,
的值始终为定值,请你求出这个定值;
【问题解决】
(3)创新小组提出一个问题,将
绕点M继续旋转,当
时,边
与
交于H,如图3,试直接写出线段
的长.
【问题情境】
学习完旋转这章内容后,在一次数学活动课上,刘老师让学生用一张矩形纸片(矩形
![](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/780372ac3d30d72fc9459827c89ba078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d108c69b0eebed90ab9a68df20b7790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9f4fe60b81ff21ca2acc95848a643d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/20/c2dc787d-20fb-42be-b683-a24b34b9b629.png?resizew=155)
【探究发现】
(1)如图2,自强小组发现,在旋转过程中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e915c7310f3781887a1afb99dbf949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a61d8bedef61745ee4fd89a8c0c119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a61d8bedef61745ee4fd89a8c0c119.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/20/03ab91c4-770e-4954-850f-ef40a9509e13.png?resizew=154)
(2)奋进小组在自强小组的基础上连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fadd86888c9722b51062bf417a8fd5e.png)
【问题解决】
(3)创新小组提出一个问题,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/20/0ebe4ced-ab92-4564-9d2c-991652cf3979.png?resizew=164)
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9 . 图,在
中,
,
平分
交
于点D,O为
上一点,经过点A,D的
分别交
,
于点E,F.
![](https://img.xkw.com/dksih/QBM/2022/4/26/2972987740037120/2979393519542272/STEM/e7eb90b0-6c76-48ad-bef8-73081c708102.png?resizew=140)
(1)求证:
是
的切线;
(2)若
,
,求
的半径;
(3)请探究
,
,
三条线段的数量关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d34e979bf61c316154f658edb3910d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2972987740037120/2979393519542272/STEM/e7eb90b0-6c76-48ad-bef8-73081c708102.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3032820a0d2d50d9143e7923f5936ddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc560914a24fb80a6608da7a188f8724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(3)请探究
![](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/6aa2b5e09f8ec785c59900a529390a02.png)
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10 . 如图,在四边形
中,
,
.点E为
边上一点,将
沿直线
折叠,使点
落在对角线
上的
处,
的延长线交直线
于点G.
![](https://img.xkw.com/dksih/QBM/2022/6/21/3012495195324416/3116043300315136/STEM/be37c687fa0f41e784d27fb9a0b6953b.png?resizew=287)
(1)求证:
;
(2)设
,
,
,探究:当四边形
为平行四边形时,
之间满足的数量关系.
![](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/c4340375ca8abdbd6998760c944f38d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/6/21/3012495195324416/3116043300315136/STEM/be37c687fa0f41e784d27fb9a0b6953b.png?resizew=287)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a81a32e4046129dd74b496dfff05ed4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5228da61bed106b28849ef91a2ec116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0786732df29e599cd67cd69e5a1a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033c1db5142bd7b60b37d276577d465b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7419886f571571b57b61a6a8980305e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba1e7a657ed134e68efd159b606620f.png)
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2022-11-23更新
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2卷引用:2020年贵州省遵义市仁怀市中考数学模拟试卷一