1 . 如图,在正方形
中,
是对角线
上的一个动点(不与点
点
重合),连接
,将
绕点
顺时针旋转
到
,连接
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f4833f39e3193cb3d77e0038e3f5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f3175a979c2f908d6c5665e14894b0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/7b8b1e0d-8c6c-4615-9fc0-2475215dd944.png?resizew=189)
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|
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2卷引用:甘肃省陇南市武都区2023-2024学年九年级上学期11月期中数学试题
2 . 如图,
中,
,点
是平面内一点,连接
并将线段
绕点
旋转至
,连接
交
于点
.
在
边上,且
,求证
;
(2)如图2,点
是
内一点,连接
、
,点
是
中点,连接
,猜想
和
的数量关系并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.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/53c98a01dc5a36ac7da9d24f96a6ca79.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/b43be568ae5186900cfb39484a3c9301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5f0e2cc2158bd508edd68e05a892b.png)
(2)如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
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4卷引用:2024年甘肃省陇南市康县部分学校九年级中考一模数学模拟试题
20-21八年级下·浙江·期末
3 . 如图,在平行四边形
中,点
分别是
的中点,点
在对角线
上,且
,连结
.求证:四边形
是平行四边形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce1475f537b4ad21775bfaa16daa0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5174e3cd2a64dfc72ed1ecfb8db5661f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1522a9c3b2466395570c2689a4055584.png)
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14卷引用:2024年甘肃省武威市凉州区武威十一中教研联片二模数学模拟试题
2024年甘肃省武威市凉州区武威十一中教研联片二模数学模拟试题2024年广东省惠州市惠城区中考三模数学试题2024年湖北省恩施州巴东县中考模拟数学试题(已下线)【新东方】 初中数学20210622-011【初二下】江苏省盐城市东台市第五教育联盟2021-2022学年八年级下学期第一次月考数学试题江苏省宿迁市沭阳县2021-2022学年八年级下学期第一次形成性测试数学试题(已下线)【浙教版课时练习】八年级下册第4章 目标与评定浙江省杭州市拱墅区大关中学教育集团2020-2021学年八年级下学期期中数学试题(已下线)9.3 平行四边形-【帮课堂】2022-2023学年八年级数学下册同步精品讲义(苏科版)(已下线)18.1.2 平行四边形的判定(含2个课时)(练习)-2022-2023学年八年级数学下册同步精品课堂(人教版)(已下线)9.3 平行四边形(第2课时)(练习)-2022-2023学年八年级数学下册同步精品课堂(苏科版)(已下线)期中真题精选(基础60题专练)-2022-2023学年八年级数学下学期期中期末考点大串讲(人教版)陕西省汉中市留坝县2021-2022学年八年级下学期期末数学试题(已下线)专题06 平行四边形(13大题型)【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(陕西专用)
名校
4 . 如图,在正方形
中,点P在对角线
上,
,
,E,F分别为垂足,连结
,
,则下列命题:①若
,则
;②若
,则
;③若正方形边长为4,则
的最小值为2,其中正确的命题是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2ef99db257cc1acb08e3a5e0006d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544204617f1eb4e26a082a72d27d0bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574dc284fb9e74d65cf0c79a978d65de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7c422a19b68b8b4cd484d22897e3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5ea309886e947ea7cb4b81716206fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c851c07c6e4b9a66e76168d6b16592e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
A.①② | B.①③ | C.②③ | D.①②③ |
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15卷引用:2022年甘肃省兰州市城关区外国语学校中考数学专项训练试卷(二)
2022年甘肃省兰州市城关区外国语学校中考数学专项训练试卷(二) 河南省郑州市郑州外国语中学2021-2022学年九年级上学期期中数学试题河南省郑州市第二中学2022-2023学年九年级上学期期中数学测试卷河南省郑州市二七区第二初级中学2022-2023学年九年级上学期期中数学试题广东省佛山市禅城区南庄中学2023-2024学年九年级上学期第一次月考数学试题 河南省焦作市中站区2023-2024学年九年级上学期期中考试数学试题浙江省宁波市鄞州区2020-2021学年八年级下学期期末数学试题河南省洛阳市2021-2022学年八年级下学期期中数学试题河南省洛阳市涧西区2021-2022学年八年级下学期期中数学试题山东省济宁市嘉祥县2021-2022学年八年级下学期期中数学试题鲁教版(五四制)八年级数学下册第六章 特殊平行四边形 单元测试题(已下线)(培优特训)专项5.2 正方形综合高分必刷题-2022-2023学年八年级数学下册《同步考点解读·专题训练》(浙教版)辽宁省盘锦市大洼区大洼区第二初级中学2021-2022学年八年级下学期期中数学试题内蒙古霍林郭勒市第五中学2023-2024学年八年级下学期期中考试数学试题(已下线)浙江省八年级期末真题必刷常考60题(60个考点专练)-2023-2024学年八年级数学下学期考试满分全攻略高频考点+重难点讲练与测试(浙教版)
真题
5 . 如图,正方形
中,点
,
分别在
,
上,且
,
与
相交于点
.
≌
;
(2)求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdc9f4a99b567a6ee4be3943beeddca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae49790c28719f3573da5d23914d325f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c434dd2ea796b34464d513a8ae7a848.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b14ee179b2f15c7c7ba0a82cdd67234.png)
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11卷引用:甘肃省定西市通渭县2023-2024学年九年级上学期学情调研测试(一)数学试题
甘肃省定西市通渭县2023-2024学年九年级上学期学情调研测试(一)数学试题甘肃省张掖市甘州中学2023-2024学年九年级上学期第一次月考数学试题2023年湖北省黄石市中考数学真题广东省惠州市惠阳区中国工农红军惠阳叶挺红军中学2023- 2024学年九年级上学期第一次月考数学试题(已下线)专题01 特殊平行四边形(考点清单,20个考点)-2023-2024学年九年级数学上学期期末考点大串讲(北师大版)贵州省六盘水市兴艺高级中学有限公司2023-2024学年九年级上学期期中数学试题(已下线)重难点03+平行四边形与特殊平行四边形(8大题型+满分技巧+限时分层检测1)-2024年中考数学【热点·重点·难点】专练(全国通用)(已下线)寒假作业13 全等三角形的基本模型(14道经典题型+4道中考真题)-【寒假分层作业】2024年八年级数学寒假培优练(人教版)(已下线)专题9.30 正方形(直通中考)(提升练)-2023-2024学年八年级数学下册基础知识专项突破讲与练(苏科版)(已下线)专题18.26 正方形(直通中考)(提升练)-2023-2024学年八年级数学下册基础知识专项突破讲与练(人教版)辽宁省营口市盖州市2023-2024学年八年级下学期期中数学试题
6 . (1)如图①,四边形
均为正方形.求证:
.
(2)如图②,四边形
均为菱形,且
.是否仍存在结论
,若不存在,请说明理由;若存在,给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20ad470fa9af2157a57c7f2de76b894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1596f7c0d0bab4e7e586d705d323e0d8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/10/a35fae74-128c-46e8-9ad4-166643784cdc.png?resizew=205)
(2)如图②,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20ad470fa9af2157a57c7f2de76b894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e6f5241f614c7d310cbf3e25a6d615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1596f7c0d0bab4e7e586d705d323e0d8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/10/f465ff6b-385b-46a5-a3af-796fb610c556.png?resizew=153)
您最近一年使用:0次
7 . 如图,在平行四边形
中,E是对角线
上的一点.连接
,
,
,求证:四边形
是菱形.
![](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/316288f967fb905834c7bb69883ad9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba11242dcc61d3c7c3555b598b5fdc89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7f1096bac944249012a68cb01930e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/4/a3ec0c97-99ba-4ca0-9469-1d60bf715bf2.png?resizew=168)
您最近一年使用:0次
2023-09-02更新
|
111次组卷
|
3卷引用:甘肃省定西市通渭县2023-2024学年九年级上学期学情调研测试(一)数学试题
名校
8 . 如图,在正方形
中,E、F分别是边
、
上的两点,且
,
、
分别交正方形的对角线
于G、H两点,将
绕点A顺时针旋转90°后,得到
,连接
.
(1)求证:
平分
;
(2)求证:
;
(3)试试探索
、
、
三条线段间的数量关系,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192155e6a3aade305b76b1eb7c75e30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/31/48d93b2b-4ca2-42d8-ac5a-59a2b332eb15.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5182d527c11a522db6d3ab5308f07b.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295111c2377037eb8d1885ae8c706968.png)
(3)试试探索
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39addc1173a458af87ed5c5e3f06466.png)
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2023-08-22更新
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91次组卷
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2卷引用:甘肃省陇南市礼县第六中学2022-2023学年九年级上学期期中数学试题
9 . 如图,在
中,
,
于点
,过点
作
于点
,交
于点
.点
在边
上,且
,连接
,延长
到点
,使
,连接
.
(1)求证:
;
(2)试判断
的形状,并说明理由;
(3)若
,
,则
________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7099026716ee1821dd7d9f157dc055f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f5dc11efe60b4fd9a13b1d6b83842.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/7e68633cbbe3cc2d0801305f81a7aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/049ba02a6816033ade98e679a59a3b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.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/149fee676220973ec0e43576b7ac1b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/13/6b0cea5a-2c6c-4868-b7bb-2d836035be57.png?resizew=332)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba36f942db248bae48c9b53344985cb.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a33d27a9c655d01f606e9bce02b0a5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65ed8e87249d3c5b9f30a89f5ded4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7facb932529ae0d511d77714cf9e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6243490cdfc0747c0cba492bd78a0758.png)
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10 . 问题背景:如图1,在等边
中,作
于点
,则
为
的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5634a7d2c5b514f8f983e081e074ca31.png)
,设
,则
,
,由勾股定理可知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37db302331272ffbe8a1cf4e77db070.png)
若将
和
重新组合为如图
的
,此时,
,
,我们可以得到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f64a2945e4f42523bf11fc742c88dc.png)
请运用此结论完成以下任务![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
迁移应用:如图
,
,
,
,
、
、
三点在同一条直线上,连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fa011a646eb1ae13ec43ba7323233b.png)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9f24820dd24c0e07f301bdfeb12c1f.png)
(2)请直接写出线段
、
、
之间的数量关系.
(3)如图4,
与
都是等边三角形,在
内作射线
,作点
关于
的对称点
,连接
并延长交
于点
,连接
、
若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8648cc68448cb78e36cff296b912ea46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/5634a7d2c5b514f8f983e081e074ca31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f60eaae8ec48911f63839c2031172ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9001f0c06cf2c8f893a38b1dabe6219e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e8cfc92fac8debb8bc06293ccc1685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9af70d46e1d13ea858ec35c0c01e06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37db302331272ffbe8a1cf4e77db070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb961bd7db3adb76af2d4cedb611bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a783e5ffcf7a4ea9e531ea76199487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394fc6a725f1f56faeff7f4ee118b082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e504b9d356ab8daa5ef17f6b61929b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bedf8995256dab614850bd4c36279b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f64a2945e4f42523bf11fc742c88dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
迁移应用:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab41054fa9ce51b68e78d9c0cf398d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a91778530fee017af63165397d36b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d959ad0bf10a92c6c6be067f7094fcb8.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/84fa011a646eb1ae13ec43ba7323233b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/29/b1721c03-589f-4345-bdbe-fb982c64ca24.png?resizew=379)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9f24820dd24c0e07f301bdfeb12c1f.png)
(2)请直接写出线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
(3)如图4,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb961bd7db3adb76af2d4cedb611bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65975206b84eba998df39052348174a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f10681704c4fccfd37664eaf34391dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e65e147b109f2bbfd3a3f502bbc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e65e147b109f2bbfd3a3f502bbc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e65e147b109f2bbfd3a3f502bbc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6417cd62cf6b5e1e46c8c0b1231c6f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10dc340e7c5a270875fcea4d3ee8873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780e1e092215e7022905b5a6f2116898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
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