1 . 如图,
和
关于直线
对称,
和
关于直线
对称.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/8ad54631-6c59-4ef3-b5b4-f93b82942308.png?resizew=149)
(1)作出直线
(尺规作图,不写作法,保留作图痕迹);
(2)直线
与
相交于点O,且直线
,
所夹锐角
,求
的度数;
(3)在(2)的条件下,小颖得出
,请你运用所学知识判断小颖的结论是否正确,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25db870913249c9cd1c48e2bd2d2f6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/8ad54631-6c59-4ef3-b5b4-f93b82942308.png?resizew=149)
(1)作出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b4189edb86626a657f2d8a57154308.png)
(3)在(2)的条件下,小颖得出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f382cb01b9ead4df16d21c3bd5c200.png)
您最近一年使用:0次
2 . 概念学习
规定:如果一个三角形的三个角分别等于另一个三角形的三个角,那么称这两个三角形互为“等角三角形”.
从三角形
不是等腰三角形
一个顶点引出一条射线与对边相交,顶点与交点之间的线段把这个三角形分割成两个小三角形,如果分得的两个小三角形中一个为等腰三角形,另一个与原来三角形是“等角三角形”,我们把这条线段叫做这个三角形的“等角分割线”.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/324d59fc-7e6e-471c-a751-e2cec1ad2f48.png?resizew=369)
(1)理解概念:判断下列说法是否正确(对的打√,错的打×)
①全等三角形是“等角三角形”()
②如图
,在
中,
,
,图中共有2对“等角三角形”()
③如图
,在
中,
,
,无论
为何值,
都不可能是
的“等角分割线”()
(2)概念应用:如图
,在
中,
为角平分线,
,
求证:
为
的等角分割线.
(3)在
中,
,
是
的等角分割线,直接写出
的度数.
规定:如果一个三角形的三个角分别等于另一个三角形的三个角,那么称这两个三角形互为“等角三角形”.
从三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/324d59fc-7e6e-471c-a751-e2cec1ad2f48.png?resizew=369)
(1)理解概念:判断下列说法是否正确(对的打√,错的打×)
①全等三角形是“等角三角形”()
②如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
③如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60742b466e878129b35628d21c2454ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)概念应用:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c5840e0454fdec7d2158072c43b8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69e456af7ab8915434bb0bd2f5b3a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a9afe4b588fccd34b74b0f765a7c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
您最近一年使用:0次
2023-11-19更新
|
46次组卷
|
2卷引用:浙江省宁波市海曙区东恩中学2023-2024学年八年级上学期期中数学试题
3 . 在七年级的学习中,我们知道:(1)三角形的内角和等于
;(2)等腰三角形的两个底角相等.下面我们对这两点知识作进一步思考和探索.
(一)三角形的外角.
三角形内角的一条边与另一条边的反向延长线组成的角,称为三角形的外角.如图1,
就是
的
的外角.在三角形的每个顶点位置都可以找到它的外角,以
为例,我们探索外角与其它角的关系.
(①__________),
(②___________)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5a716592d862464b3ff814e45d0e11.png)
(③__________)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635b1af26e27be60f4cf4817e6d4e1d9.png)
由此我们得到了三角形外角的两条性质:
(1)三角形的一个外角等于和它不相邻的两个内角的和.
(2)三角形的一个外角大于任何一个和它不相邻内角.
问题1:
(1)请在以上括号①②③中填上适当的理由;
(2)请在图1中分别画出
和
的一个外角,并分别标注为
,
.
(二)等腰三角形的两个底角相等.
等腰三角形的两个底角相等,我们简述为“等边对等角”,数学小组据此提出问题:三角形中大边对的内角也大,即“大边对大角”正确吗?小聪同学进行了如下探索.
问题2:
如图2,
中
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24a07ee331866778ea413e465a4f0ce.png)
证明:如图3,在
边上截取
,连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f05dfb173e003ab30d2a424b96637.png)
(④__________)
(整体大于部分)
又
(⑤_________)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314df17ec77fb1e71d07c1c9cd9574d0.png)
由此说明三角形中大边对大角.
请在以上括号④⑤中填上适当的理由.
问题3:
如图4,
中
,
,请判断
是否成立,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e7a123c9cc0e058db28841fb0edcf3.png)
(一)三角形的外角.
三角形内角的一条边与另一条边的反向延长线组成的角,称为三角形的外角.如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/6ea8918a-30b6-42e6-8480-e3af911e746c.png?resizew=204)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4280c3963b4900adb983db9a3a4b58ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a1b09bae4841be75f196673a627497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffc2f065a5d5febb87359016eac379d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5a716592d862464b3ff814e45d0e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d0f3991ab2d191e46e36e3072388b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d17adae48fae0dea0ab332763dc91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635b1af26e27be60f4cf4817e6d4e1d9.png)
由此我们得到了三角形外角的两条性质:
(1)三角形的一个外角等于和它不相邻的两个内角的和.
(2)三角形的一个外角大于任何一个和它不相邻内角.
问题1:
(1)请在以上括号①②③中填上适当的理由;
(2)请在图1中分别画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605f2976297a0deaa1602ef09d6a5afa.png)
(二)等腰三角形的两个底角相等.
等腰三角形的两个底角相等,我们简述为“等边对等角”,数学小组据此提出问题:三角形中大边对的内角也大,即“大边对大角”正确吗?小聪同学进行了如下探索.
问题2:
如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb980da8e86b4cfd322616dc84fc6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24a07ee331866778ea413e465a4f0ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/dec32640-3e28-4f44-b8f0-5bafff271626.png?resizew=127)
证明:如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc13fe21e64d9b45614ed43be847904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/aaa65144-a2b8-4e26-b3e4-7420e387dd04.png?resizew=128)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f05dfb173e003ab30d2a424b96637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d98228bd5ecb89ef69c62a71f8e1ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6818402824ac026a750a8bcc4c2db372.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd37e385a92dc12298ae8278cf58386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314df17ec77fb1e71d07c1c9cd9574d0.png)
由此说明三角形中大边对大角.
请在以上括号④⑤中填上适当的理由.
问题3:
如图4,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c251ed1472ba56f13a80abbfeb06c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9af7ab732d431dd78e84db9586d3cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/f79f2beb-bbf5-4925-b9e3-721596dd078b.png?resizew=128)
您最近一年使用:0次
4 . 阅读下列材料,完成相应任务.
【探究三角形中边与角之间的不等关系】
学习了等腰三角形,我们知道在一个三角形中,等边所对的角相等;反过来,等角所对的边也相等,那么,不相等的边所对的角之间的大小关系怎样呢?大边所对的角也大吗?下面是奋进小组的证明过程.
如图1,在△
中,已知
.求证
.
![](https://img.xkw.com/dksih/QBM/2022/10/15/3088002471641088/3089693671415808/STEM/d033c0b3b9554055851196a8ce9611f0.png?resizew=298)
证明:如图2,将△
折叠,使边
落在
上,点
落在
上的点
处,折痕
交
于点
.则
.
∵
________
(三角形外角的性质)
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b487f865bfb4750eee61bf9ec5059f.png)
∴
(等量代换)
类似地,应用这种方法可以证明“在一个三角形中,大角对大边,小角对小边”的问题.
(1)任务一:将上述证明空白部分补充完整;
(2)任务二:上述材料中不论是由边的不等关系,推出角的不等关系,还是由角的不等关系推出边的不等关系,都是转化为较大量的一部分与较小量相等的问题,再用三角形外角的性质或三边关系进而解决,这里主要体现的数学思想是________;(填正确选项的代码:单选)
A.转化思想 B.方程思想 C.数形结合思想
(3)任务三:根据上述材料得出的结论,判断下列说法,正确的有________(将正确的代码填在横线处:多选).
①在△
中,
,则
;
②在△
中,
,
,则△
是锐角三角形;
③
△
中,
,则最长边是
;
④在△
中,
,
,则
.
【探究三角形中边与角之间的不等关系】
学习了等腰三角形,我们知道在一个三角形中,等边所对的角相等;反过来,等角所对的边也相等,那么,不相等的边所对的角之间的大小关系怎样呢?大边所对的角也大吗?下面是奋进小组的证明过程.
如图1,在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5bac918d34537ff02a518a63031aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaaae5a489951101a9c06fd94ff523d6.png)
![](https://img.xkw.com/dksih/QBM/2022/10/15/3088002471641088/3089693671415808/STEM/d033c0b3b9554055851196a8ce9611f0.png?resizew=298)
证明:如图2,将△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77936a859f39507de5a2d3070b13a60a.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/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3256a9f3b49b8e60ce44e8deec42d822.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b28daad9a051987ab64dc8a299d42bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66cb5797ef6c0853368ca92df9e5402b.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b487f865bfb4750eee61bf9ec5059f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaaae5a489951101a9c06fd94ff523d6.png)
类似地,应用这种方法可以证明“在一个三角形中,大角对大边,小角对小边”的问题.
(1)任务一:将上述证明空白部分补充完整;
(2)任务二:上述材料中不论是由边的不等关系,推出角的不等关系,还是由角的不等关系推出边的不等关系,都是转化为较大量的一部分与较小量相等的问题,再用三角形外角的性质或三边关系进而解决,这里主要体现的数学思想是________;(填正确选项的代码:单选)
A.转化思想 B.方程思想 C.数形结合思想
(3)任务三:根据上述材料得出的结论,判断下列说法,正确的有________(将正确的代码填在横线处:多选).
①在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df19eae422a11ecd874c01ce3d68178e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1494d156b2751301baf97ca7746cc971.png)
②在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69d51f1998b6335cc7323b37537c251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d36d0c89e9b5abbe28a7dad2468ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7eccdc904f71a7a6a02134f47e08072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9429e394d7cf08f2cdbc7f1be7dfaaec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
④在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aca429d9688fa2721280ae7d7a00b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a691a85ae5a0bc49d3c411926ee1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63dee45a1084de33934b9abb6bed96ad.png)
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5 . 数学老师在课上呈现一个几何图形,如图,∠1=∠2,AB⊥CD于点E,过点E作一条直线分别交线段BC,AD于点F,G.同学们根据图形进行大胆猜想.小方说:当∠3=∠1=50°时,可求得∠CFE的度数.小何说:当BF=CF时,可证得EG⊥AD.
(1)依据小方说的条件,你求得∠CFE= .(直接写出答案)
(2)依据小何说的条件,请你判断他的结论是否正确,并说明理由.
(1)依据小方说的条件,你求得∠CFE= .(直接写出答案)
(2)依据小何说的条件,请你判断他的结论是否正确,并说明理由.
![](https://img.xkw.com/dksih/QBM/2021/12/19/2875636560732160/2877182165983232/STEM/9efd61387bfd458a9159b3800c0a92a3.png?resizew=197)
您最近一年使用:0次
20-21八年级上·浙江杭州·期末
6 . 如图,在
中,
,
是高线,
,
,
(1)用直尺与圆规作三角形内角
的平分线
(不写作法,保留作图痕迹).
(2)在(1)的前提下,判断①
,②
中哪一个正确?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68d1411b29141ea7fc377b44ad92611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6988b81937a2b98659c359d9ed686146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96128255fefba0cd356cf9562588f148.png)
(1)用直尺与圆规作三角形内角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)在(1)的前提下,判断①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6158a9585facfd09a35bea075fcfcbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fce96c6ca87df2e1ce8d481fa59ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/3/be392930-9f46-4a3c-82dd-920c23ccfbbe.png?resizew=213)
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2020-01-12更新
|
159次组卷
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3卷引用:【新东方】【杭州】10【2020年】【初二上】【期末考】