名校
1 . 如图,在
中,
,
,
的垂直平分线分别交
和
于点D,E.
;
(2)连接
,直接写出
的形状:___________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8572e7aa6d36113cc5ed43c47035378f.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
您最近一年使用:0次
2024-04-12更新
|
263次组卷
|
47卷引用:重庆市南岸区2017-2018学年八年级下学期期末数学试题
重庆市南岸区2017-2018学年八年级下学期期末数学试题重庆市荣昌区2022-2023学年八年级上学期期末数学试题华师大版八年级数学上册单元测试 第13章 全等三角形人教版八年级上册数学 第十三章 轴对称 单元测试2018-2019学年八年级数学下册北师大版习题:期中检测卷广东省深圳市南山区2018-2019学年八年级下学期期末数学试题广东省汕头市汕头聿怀实验学校2019-2020学年八年级上学期期中数学试题江苏省南通市南通市北城中学2019-2020学年八年级上学期第一阶段考数学试题陕西省西安市莲湖区2018-2019学年八年级下学期期中数学试题广东省深圳市龙岗区智民实验学校2019-2020学年八年级下学期期中数学试题(已下线)期末押题预测05(B卷) -2020-2021学年八年级数学下学期期末专项复习(北师大版,广东专用)(已下线)【北师大版课时练习】 八年级下册 第一章 三角形的证明 复习题河南省驻马店市部分校2021-2022学年八年级下学期第一次学情反馈数学试题广东省揭阳市2021-2022年八年级下学期第三阶段综合数学试题辽宁省沈阳市第一三四中学2021-2022学年八年级下学期期中数学试题辽宁省丹东市东港市2021-2022学年八年级下学期期末数学试题广东省深圳市龙岗区龙城初级中学2021-2022学年八年级下学期期中数学试卷江西省吉安市吉州区兴桥中学2021-2022学年八年级下学期中数学试题(已下线)期中真题精选(常考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(北师大版)贵州省贵阳市第四十中学2022-2023学年八年级下学期3月月考数学试题广东省揭阳市揭西县凤江中学2022-2023学年八年级下学期5月月考数学试题吉林省长春市榆树市八号镇中学2022-2023学年八年级下学期5月联考数学试题山东省青岛市黄岛区2022-2023学年八年级下学期期末数学试题山东省青岛市胶州市2022-2023学年八年级下学期期末数学试题山东省青岛市李沧区、黄岛区、胶州市2022-2023学年八年级下学期期末数学试题山东省青岛市李沧区2022-2023学年八年级下学期期末数学试题辽宁省沈阳市和平区2022-2023学年八年级下学期期末数学试题辽宁省沈阳市和平区第一三四中学2022-2023学年八年级下学期期中数学试题江苏省苏州市吴中区华中师范大学苏州实验中学2023-2024学年八年级上学期9月月考数学试题(已下线)专题02 轴对称图形(知识串讲+热考题型+真题训练)-2023-2024学年八年级数学上学期期中期末考点归纳满分攻略讲练(苏科版)福建省龙岩市新罗区龙岩市第二中学2023-2024学年八年级上学期月考数学试题吉林省松原市前郭县三校联考2023-2024学年八年级上学期期中数学试题吉林省吉林市昌邑区第九中学2023-2024学年八年级上学期期中数学试题湖南省永州市道县绍基学校2023-2024学年八年级上学期期末模拟数学试题(已下线)期末真题精选(常考60题33个考点分类专练)(原卷版)山西省忻州地区2023-2024学年八年级上学期期中数学试题(已下线)YHmlsjsxXJ860.pdf湖南省长沙市立信中学2023-2024学年八年级上学期第三次月数学试题(已下线)清单03 轴对称 (16个考点梳理+典型例题+核心素养提升+中考热点聚焦)-2023-2024学年八年级数学上学期期末考点大串讲(人教版)四川省成都市锦江区成都金苹果锦城第一中学2022-2023学年八年级下学期期中数学试题山东省枣庄市滕州市北辛街道北辛中学2023-2024学年八年级下学期第一次质量检测月考数学试题河南省平顶山市汝州市2023-2024学年八年级下学期期中数学试题吉林省松原市前郭县乡镇联考2023-2024学年八年级下学期期中数学试题吉林省桦甸市第七中学2023-2024学年八年级下学期期中考试数学试题(已下线)专题01 直角三角形(8大题型+优选提升题)-备战2023-2024学年八年级数学下学期期末真题分类汇编(湖南专用)2023年山东省淄博市临淄区中考一模数学试题山东省淄博市临淄区2022-2023学年七年级下学期期末数学试题(五四学制)
名校
2 . 如图,点
是矩形
的边
延长线上一点,连接
交
于点
,
.
,使
交线段
于点
,连接
;(保留作图痕迹,不写作法)
(2)在(1)的基础上,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665f6fb409d3b29c9bd0459f8b9fb064.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/d831c9ba6d18774540e2aaa29132fec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d69f2006b1fcd949e557fd83f88a895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
(2)在(1)的基础上,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bca927b232649d457422447fc71bc10.png)
您最近一年使用:0次
3 . 在学习完勾股定理后,喜欢思考的小明想进一步探究直角三角形斜边的中线,他的思路是:
在中,先作出直角边
的垂直平分线,并猜测它与斜边
的交点是中点,于是他把交点与点
连接,通过垂直平分线的性质以及等角对等边的代换,他发现了直角三角形斜边的中线与斜边的数量关系.
请根据小明的思路完成以下作图与填空:
用直尺和圆规作的垂直平分线交
与点
,垂足为点
,连接
.(保留作图痕迹,不写作法)
已知:在中,
°,
垂直平分
,垂足为点
.
求证:.
证明:∵垂直平分
,
∴________,
∴.
∵在中,
,
∴,
________
,
∴,
∴________,
∴.
∴.
通过探究,小明发现直角三角形均有此特征,请依照题意完成下面命题:直角三角形斜边的中线________.
由此易解决以下问题:若的周长为24,
,
,则
边上的中线长为________.
您最近一年使用:0次
名校
4 . 如图,在
中,
是对角线.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/26/7e1b24fe-797b-4a55-933c-1c1acfe399ed.png?resizew=182)
(1)尺规作图:作线段
的垂直平分线
,分别交
、
、
于点
、
、
,连接
和
(用尺规作图,并在图中标明相应的字母,保留作图痕迹);
(2)在(1)的条件下,求证四边形
是菱形(请补全下面的证明过程,将答案写在答题卡对应的番号后).
证明:∵
垂直平分
,
∴
.
又∵四边形
是平行四边形,
∴①________
∴
.
在
和
中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb286a47dbde46677a8619f548d5c151.png)
②________
∴
,
∴③________
∵
垂直平分
,
∴
,④________
∴
,
∴四边形
是菱形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/26/7e1b24fe-797b-4a55-933c-1c1acfe399ed.png?resizew=182)
(1)尺规作图:作线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
(2)在(1)的条件下,求证四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bdae3d30abf70515bdbd45f9d0c380.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9ea68dbddf33f0fed8f35a1fd5c90b.png)
又∵四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
∴①________
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6e5c05ccd9a271f2f253a053502615.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c525358262126a51fbb598d58f3e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74625390340982140e449e07663579a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb286a47dbde46677a8619f548d5c151.png)
②________
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a49fc8b7061e74c854ae12908a95b0.png)
∴③________
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba11242dcc61d3c7c3555b598b5fdc89.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671eab9d0b5621d93972b7e62b816766.png)
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bdae3d30abf70515bdbd45f9d0c380.png)
您最近一年使用:0次
5 . (1)如图1,在
中,
,
边上的垂直平分线
交
于点D,交
于点E,连接
,
将
分成两个角,且
,求
的度数.
(2)如图2,
中,
、
的三等分线交于点E、D,若
,
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce7f6d278f2ef7a193b7eed7be6b3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/f52a58fbaf4fea03567e88a9f0f6e37e.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/21b28f28ced0531d1df34fcf04c6c67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9d120f194183358b94b99c4376e402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756eb9a840789a7b4b265aa5b2d2958a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6aecc788824453d80546bf649c077fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
您最近一年使用:0次
2024-03-22更新
|
81次组卷
|
5卷引用:重庆市渝北区渝北区实验中学校2023-2024学年八年级上学期期中数学试题
重庆市渝北区渝北区实验中学校2023-2024学年八年级上学期期中数学试题广东省湛江市霞山区银帆学校2023-2024学年八年级上学期期中数学试题广东省湛江市霞山区滨海学校2023-2024学年八年级上学期期中数学试题(已下线)专题01 三角形的证明(考点清单,知识导图+7个考点清单、题型解读)-2023-2024学年八年级数学下学期期中考点大串讲(北师大版)(已下线)猜想01 三角形(考题猜想,常考易错7个考点42题专练)-2023-2024学年八年级数学下学期期中考点大串讲(北师大版)
名校
6 . 在“轴对称”的学习中,小明遇到一个有趣的问题:在
中,
,
,试将
分割成三个形状、大小完全相同的三角形并证明.小明的思路是:构造该直角三角形斜边的中垂线,与
角所对的边相交,再连接该交点与
角的顶点即完成分割,利用线段中垂线的性质及三角形全等进行证明.请结合小明的思路完成下面的作图与填空:直尺 和圆规 作边
的垂直平分线,分别与
,
相交于点
,
,连接
.(只保留作图痕迹,不写作法)
垂直平分边
且
在边
上,
,
.
在边
的垂直平分线上,
___________①___________.
又
,
___________②___________
.
,
,
___________③___________.
.
又
___________④___________,
.
则分成的
,
,
的形状、大小完全相同.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1949518fc246fbd8426d08f701ade25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b69adc1aff19a9b4277c46d471ec12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb64353c99068a7a1a8508a22f5b25b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b443ca71c0e64c15c0ec2b9b65b607c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda91c138a9d926edaaab3295f1d7b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b8082bcd1d00673ec51214a750f2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5ec6ae60e65b8e9e4535d7ed8824be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1578c2e2b695e1e96cc454b6d4cb83.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b39803dce3beb6ef2d7bc5c6a61933a.png)
则分成的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15514bc735fe4b744672edefe00009c.png)
您最近一年使用:0次
2024-03-22更新
|
38次组卷
|
2卷引用:重庆市第九十四初级中学校2023-2024学年八年级下学期期中考试数学试题
名校
7 . 如图,在菱形
中,
,取大于
的长为半径,分别以点
为圆心作弧相交于点
,连接
,则
的度数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d49404351575703cfe8325d1352ec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fc4fa377fc18a46781c3ad37df9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e359bc7a47c723102813220ef7283177.png)
您最近一年使用:0次
2024-03-16更新
|
187次组卷
|
3卷引用:重庆市求精中学校2023-2024学年八年级下学期期中数学试题
8 .
中,
,
,
的垂直平分线交
于
,交
于
,点
为
边的中点,
为直线
上一点,则
周长的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f138deab9e5a4baaada287ed1a78df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e323c08b18488d11bd8f3cd74efa971a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/41b85aab-d6d9-455d-8166-0b781556d3e3.png?resizew=222)
您最近一年使用:0次
9 . 已知,如图,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/a14638de-6158-4b6c-b190-9b54f40266f1.png?resizew=147)
(1)用尺规完成以下基本作图,作线段
的垂直平分线,交
于
,交
于
,连接
(不说明理由,不下结论,只保留作图痕迹).
(2)在(1)所作的图形中,求证:
.
涵涵的思路是这样:由垂直平分线的性质得到
,从而得到
,再证明
,从而得到
,最后由等量代换可得
.请根据这个思路补全下面的证明过程.
证明:
直线
是线段
的垂直平分线
①_______,
②_______,
,
,
③_______
,
,
④_______,
,
⑤_______,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c62b53d8bf190fec68780760a0abf6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/a14638de-6158-4b6c-b190-9b54f40266f1.png?resizew=147)
(1)用尺规完成以下基本作图,作线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)在(1)所作的图形中,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98de02d1d5b7ac04bce54be393218922.png)
涵涵的思路是这样:由垂直平分线的性质得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd260fb9d772c122dcb1df52cbe38ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897c3bec4b7e2be338c6faf41442f27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57cb0d726cc25a350dc792b539ff2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3a6dcaf9f9e9a940b4a16f7ec2fc2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc1a8e1de618493faf62d1e75638a49.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.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/b5f96d400f5d5f0a40f17048dc0fa480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c435479c550284ac5efe46c903cabf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6808b55943e0ab815da922bf1b095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c703ae2d0e1ee513be258e74591de40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71ce56e2fc5d86da9e55aee4ec50719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd8b904875a181c2b29d3cd8e0c5d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9132da6876ce3c9bbdfa72685b56fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abe737bbb163965180279b0fcb1da27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b48d65c6d7eb6853a644642307ee3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c8507788be312503cc9ac63178c60c.png)
您最近一年使用:0次
10 . 如图,在
中,
的垂直平分线分别交
于点D,E,连接
.若
,
的周长为
,则
的周长为 _______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73721d69c3c3dece2996af8bd6a0052f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19daa2b38e3a52bd7096d235c843110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/2045f6b2-1087-41a8-a10c-0fe8b6766d57.png?resizew=138)
您最近一年使用:0次