名校
1 . 如图,在
中,
,
,
,
垂直平分
,点D为直线
上的任意一点,则
周长的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae8221601c7bd5c51fd520615581fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
您最近一年使用:0次
2024-01-03更新
|
184次组卷
|
10卷引用:重庆市九龙坡区杨家坪中学2023-2024学年八年级上学期期中数学试题
重庆市九龙坡区杨家坪中学2023-2024学年八年级上学期期中数学试题山东兰陵芦柞初中2020-2021学年八年级上学期期中数学试题湖北省省直辖县级行政单位潜江市2020-2021学年八年级上学期期末数学试题湖北省天门市2020-2021学年八年级上学期期末数学试题(已下线)专题1.6 线段的垂直平分线(专项练习)-2020-2021学年八年级数学下册基础知识专项讲练(北师大版)(已下线)专题13.16 课题学习——最短路径问题(基础篇)(专项练习)-2022-2023学年八年级数学上册基础知识专项讲练(人教版)(已下线)13.4 课题学习 最短路径问题(练习)-2022-2023学年八年级数学上册同步精品课堂(人教版)广东省茂名市高州市第一中学附属实验中学2022-2023学年七年级下学期5月月考数学试题(已下线)专题5.15 将军饮马模型(知识梳理与考点分类讲解)-2023-2024学年七年级数学下册基础知识专项突破讲与练(北师大版)(已下线)第5章 生活中的轴对称(单元测试·基础卷)-2023-2024学年七年级数学下册基础知识专项突破讲与练(北师大版)
名校
2 . 如图,在
中,
是
的垂直平分线,
,
的周长为11,则
的周长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/8aae537d-8df0-4aec-bed4-6b1efe4e2af8.png?resizew=157)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b418586278f75e20ee56a86e24cb2601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb961bd7db3adb76af2d4cedb611bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/8aae537d-8df0-4aec-bed4-6b1efe4e2af8.png?resizew=157)
A.14 | B.17 | C.19 | D.20 |
您最近一年使用:0次
3 . 如图,已知:在
中,
,
于点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/32ec8b12-4b0f-4e14-b5fb-a2c7fd4f9739.png?resizew=150)
(1)尺规作图:作线段
的垂直平分线交
于点E,交
于点F,连接
(不写作法,保留作图痕迹);
(2)求证:
.
证明:∵
,
∴
① ,
∵
是
的垂直平分线,
∴
② ,
∴
,
∴
,
即
③ ,
∵
,
∴ ④
,
∴
,
∴
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/32ec8b12-4b0f-4e14-b5fb-a2c7fd4f9739.png?resizew=150)
(1)尺规作图: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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e06268afbd3701864038813c3e44be.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db07c6ce6c8b0e96a3470c6a3491334.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7fa9d70f03e1206629649addd8dddc.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86f847b4da613c90a7bdefcd994006.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af015f7ef349e2fc46a703ff6020e247.png)
即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863c4a2e68dae7f51ae92052e830f73b.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
∴ ④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475ff337241b4234463c699219007738.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838165d7e5f450e45e0ac29c608f0dc1.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e06268afbd3701864038813c3e44be.png)
您最近一年使用:0次
4 . 如图,在
中,
的角平分线交
于点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/54797cfa-f0eb-4e94-a926-08d8f15c881e.png?resizew=149)
(1)用尺规完成以下基本作图:作
的垂直平分线分别与
、
、
交于点E、点F、点H.(保留作图痕迹,不写作法)
(2)在(1)所作的图形中,连接
、
,完成下面证明
的过程.
证明:∵
的角平分线交
于点D,
∴
______.
∵
垂直平分
,
∴
,
______,______,
∴
,
∴
,
∴
______
.
∴
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/54797cfa-f0eb-4e94-a926-08d8f15c881e.png?resizew=149)
(1)用尺规完成以下基本作图:作
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)在(1)所作的图形中,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f43ee6bef36a3a67b497cb2e67f4df.png)
证明:∵
![](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/1c0c46783b77cce2bd4b45b9acc61884.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4790b2cd75df9633fe25e9df427cc441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e776314d1f1670d3a90f2a35125feb67.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97628c76d57d4314682a1fd51fa9750.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28580daa12f77508922012510f533db.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0780d075235fe5a85b550d06df0edef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9039defba7c11afba53baa22392b676.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f43ee6bef36a3a67b497cb2e67f4df.png)
您最近一年使用:0次
2023-12-28更新
|
59次组卷
|
2卷引用:重庆市重庆市华东师范大学附属中旭科创学校2023-2024学年八年级上学期期中数学试题
5 . 如图,矩形
中,E为
的中点,连结
,过E作
交
点F,连结
,若
,则
的度数为( )
![](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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a19339adac3a2f1aab1fbc11b1c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/decaaa999bfb7d74d1d69a3dd2be0a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53a92b465cdbfa308a8bd5e35d2bd27.png)
A.α | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-27更新
|
210次组卷
|
3卷引用:重庆市开州区文峰教育集团2023-2024学年九年级上学期12月月考数学试题
重庆市开州区文峰教育集团2023-2024学年九年级上学期12月月考数学试题(已下线)专题03 八下特殊四边形综合题专练(6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(浙江专用)浙江省金华市南苑中学2023-2024学年八年级下学期期中数学试题
名校
6 . 如图,在
中,
,
,
,
边的垂直平分线交
于E,交
于D,F为
上一点,连接
,点C关于
的对称点
恰好落在
的延长线上,则
的长为 __________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900b844294e8c07ea9a858adb845121c.png)
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2023-12-24更新
|
851次组卷
|
10卷引用:重庆市渝中区巴蜀中学校2022-2023学年八年级上学期期末数学试题
重庆市渝中区巴蜀中学校2022-2023学年八年级上学期期末数学试题重庆市第八中学2023-2024学年八年级上学期数学期末模拟试题(已下线)专题18.16 勾股定理(方程思想)(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(沪科版)(已下线)专题18.22 用勾股定理解直角三角形(知识点分类专题)(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(沪科版)(已下线)专题17.22 用勾股定理解直角三角形(知识点分类专题)(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(人教版)(已下线)专题17.16 勾股定理(方程思想)(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(人教版)辽宁省大连甘井子区第八十中学、第七十六中学2022-2023学年九年级下学期3月月考数学试卷湖南省郴州市2022-2023学年八年级下学期开学考试数学试题(已下线)八年级上学期期末模拟测试卷01-2023-2024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)(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)——专题二—勾股定理
名校
7 . 当已知三角形一边中点时,我们常通过“倍长中线”来构造全等的两个三角形,从而解决问题.
已知
,点
是
的中点.
(1)如图1,点
在
上,延长
交
于点
,且
,求证:
;小明同学应用倍长中线的方法,延长
至点
,使
,连接
,请你帮助他写出证明过程;
(2)如图2,点
在射线
上,连接
,延长
交
于点
,若
为
的中点,求证:
;
(3)在(2)的条件下,若点
是线段
的中点,
垂直平分线段
,在
上有一动点
,连接
,当
的周长最小时,直接写出
的度数.
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/7aeb203a-0963-4be0-abfa-c4215a74cb47.png?resizew=578)
(1)如图1,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.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/af8bfe298fb2948547723517cd2ec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b59f0e6f7fa9c50e7f5cc146ba1af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5710961e98c6811400da2c0b778d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
(2)如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52041559f8fee18bfa3e2e2ac07c3bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194726b486d1b544f28392cd89ddcbb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee1b5f29deb1c42e4ee9370e0a30c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a6f7091bf0bb4b27a436d7cc29ca9d.png)
(3)在(2)的条件下,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766c0b7b584766b8b376e89621b4e7c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a5bbcebfe4655fe2a73b50c002118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbb6763c631d9680525050c76218124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4257874d7910eb357589dc1954bdf76.png)
您最近一年使用:0次
2023-12-22更新
|
793次组卷
|
2卷引用:重庆市九龙坡区育才中学校2023-2024学年八年级上学期数学第七次自主作业
8 . 如图,在
中,
平分
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/4f170d67-72fa-4e13-baf7-54751e36a405.png?resizew=242)
(1)用尺规完成以下基本作图:过点
作
于点
,交
于点
,连接
;(不写作法,不下结论,保留作图痕迹)
(2)求证:
,请根据下列证明思路完成填空:
证明:
____________,
.
于点
,
(____________)
在
和
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229ad9e4aa38b247f1abf8f938280852.png)
(____________).
____________
是线段
的垂直平分线
(____________)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/4f170d67-72fa-4e13-baf7-54751e36a405.png?resizew=242)
(1)用尺规完成以下基本作图:过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d6b98ecb4793c9f063f1f6b61caa19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad98ad714864041a632ca949308e417.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113bffa74ac1e976a5c468ccde2dc860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f75cd01b3689408ebb2bcea4b25f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d257e50f224710383ad7a1b2da603d4.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d671ea595b1a638992a531471ab47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022f0dc17db5fcc83b204dc845447ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229ad9e4aa38b247f1abf8f938280852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87d978d02e1ccc8112746d456dcbab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56577eaa2f4ed14e6e4330a801a59293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a860c6ab2c48b1c458f54fdb23fa8bd.png)
您最近一年使用:0次
名校
9 . 如图,
是
的垂直平分线,
,
的周长是
,则
的周长是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/411e758a-3c6b-4853-addc-4a4131bc0283.png?resizew=193)
![](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/7cee49e97546d466ba3ee630e08cdc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff748d864eeeefef79124c297c0675c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/411e758a-3c6b-4853-addc-4a4131bc0283.png?resizew=193)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-19更新
|
120次组卷
|
2卷引用:重庆市开州区文峰教育集团2023-2024学年八年级上学期12月月考数学试题
名校
10 . 如图,已知四边形
中,
为
边上一点,连接
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/57413150-be9b-4eda-bf84-0ad1e2dfcede.jpg?resizew=170)
(1)用直尺和圆规完成以下基本作图:过点
作
的垂线交
于
(保留作图痕迹);
(2)在(1)的条件下,若
,
,
为
的角平分线.
求证:
.完成下列填空.
证明:∵
,
,
①____________,
,
为
的角平分线,
,
②____________,
,
,
即:③____________,
∴
④____________,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/57413150-be9b-4eda-bf84-0ad1e2dfcede.jpg?resizew=170)
(1)用直尺和圆规完成以下基本作图:过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e472dea21dbfb4ab929e970d4bcbcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd9f2ab635fbcde5f49a7919fe0b8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38968daa1e0f0a5caceb3ede903105ad.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7de19ceb054d778b94d849337d8a02.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f5dc11efe60b4fd9a13b1d6b83842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e472dea21dbfb4ab929e970d4bcbcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8cbe6e341b308d8551751e2c6b3c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671c73a48dfce4894545ae665b17f77d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c38ffc474f45993a7ed1e3cd5da75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579b7a12dffd2b0be7ad5fa4ec9106e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0eccaabe3cd78d3974282019505fb9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353ab7837467b911fcc5983af6339793.png)
即:③____________,
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8a9dedc0ea544bcdc304a6f6016aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0268b7417bbdd8a53d0659399a6a8317.png)
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