1 . 对于特殊四边形,通常从定义、性质、判定、应用等方面进行研究,我们借助于这种研究的过程与方法来研究一种新的四边形——筝形.
定义:在四边形中,若
,我们把这样四边形
称为筝形.
性质:按下列分类用文字语言填写相应的性质:
从对称性看:筝形是一个轴对称图形,它的对称轴是______;
从边看:筝形有两组邻边分别相等;
从角看:______;
从对角线看:______.
判定:按要求用文字语言填写相应的判定方法,补全图形,并完成方法2的证明.
方法1:从边看:运用筝形的定义;
方法2:从对角线看:______;
如图,四边形中,______.求证:四边形
是筝形.
应用:如图,探索筝形的面积公式______(直接写出结论).
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2卷引用:贵州省遵义市遵义市十校2023-2024学年期末模拟联考数学试题
2 . 如图,正方形网格中的每个小正方形边长都是1,每个小正方形的顶点叫做格点.
、
,画线段
使它与
、
组成轴对称图形(画出所有符合题意的线段);
(2)在图②中,找一格点D,使它到
、
的距离相等,到点A、C的距离也相等.(找到D点即可,不写过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)在图②中,找一格点D,使它到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
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3 . 如图,在
中,
是
的垂直平分线,
,且
,则
的周长为_______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6747441b260ca043446b5d472fece440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6d6597d07c8e98ca0c21d2527942ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/f9c6dc70-8cba-48a7-8499-dbea7c5fc484.png?resizew=164)
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4 . 如图,解答下列问题∶
(1)写出
三点的坐标.
(2)若
各顶点的纵坐标不变,横坐标都乘
,请你在同一坐标系中描出对应的点
,并依次连接这三个点,所得的
与
有怎样的位置关系?
(3)找一点
,使得点
到
两点距离相等且直线
垂直于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/a151a0a1-adfa-4edf-92e4-42974f7bdd5b.png?resizew=240)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d100e7830d2e9d27bdccb181c79b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)找一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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2卷引用:江苏省淮安市盱眙县第三中学2023-2024学年八年级上学期12月月考数学试题
5 . 如图,在
中,
,
,
,
是
边上的高,若
,
分别是
和
上的动点,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eeb0c8df3d8c5260768c5e407b3583a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b939af5ba06e279cce39396aaf0fae06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ee826937d2add7a93aaa1422f8b736.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5d464faee7d43274109aa13698fa48.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/d4dae923-da85-4b90-b2bc-e9dc7f1f8b63.png?resizew=167)
A.2.4 | B.4.8 | C.7.2 | D.9.6 |
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解题方法
6 . (1)阅读理解:如图1,在
中,若
,
.求
边上的中线
的取值范围,小聪同学是这样思考的:延长
至
,使
,连接
.利用全等将边
转化到
,在
中利用三角形三边关系即可求出中线
的取值范围,在这个过程中小聪同学证三角形全等用到的判定方法是______,中线
的取值范围是______;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/cc708eae-08b2-424e-8a91-f03663bbd38d.png?resizew=141)
(2)问题解决:如图2,在
中,点
是
的中点,
.
交
于点
,
交
于点
.求证:
;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/ba5c0c1c-e629-4c92-bb12-bfff64bee161.png?resizew=153)
(3)问题拓展:如图3,在
中,点
是
的中点,分别以
,
为直角边向
外作
和
,其中
,
,
,连接
,请你探索
与
的数量与位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad98ad714864041a632ca949308e417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09a769a75b107390b9eeccc929f761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/cc708eae-08b2-424e-8a91-f03663bbd38d.png?resizew=141)
(2)问题解决:如图2,在
![](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://staticzujuan.xkw.com/quesimg/Upload/formula/e47f2874795e9df280e3e0bec171358e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b01908bf059263d6548ea1ec12be20.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/ba5c0c1c-e629-4c92-bb12-bfff64bee161.png?resizew=153)
(3)问题拓展:如图3,在
![](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://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ebc9a7a29f686f4288c70391897b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1029f5256edc6652fc4efb87f6b55569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94db851a2a0c17afbb635820dcf552f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7115b9ba0494ead745fc91f6b145e8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217ae5ea057e69f31439fef55812c851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/b8e5280a-2069-45c3-ae48-9ec652f217b9.png?resizew=166)
您最近一年使用:0次
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15卷引用:广东省汕头市金平区2022-2023学年八年级上学期期末数学试题
广东省汕头市金平区2022-2023学年八年级上学期期末数学试题甘肃省定西市安定区思源实验学校2022-2023学年八年级上学期期末考试数学试题(已下线)专题04 全等三角形模型训练(6类经典模型+优选提升)-【好题汇编】备战2023-2024学年八年级数学上学期期中真题分类汇编(人教版)山东省德州市庆云县渤海中学2023-2024学年八年级上学期第一次调研数学试题湖北省武汉市江岸区武汉市培英中学2023-2024学年八年级上学期月考数学试题广东省惠州市第五中学2023-2024学年八年级上学期期中数学试题(已下线)12.3(培优课)倍长中线(题型精讲精练)-【题型分类精粹】2023-2024学年八年级数学上学期期中期末复习讲练系列【考点闯关】(人教版)广东省珠海市香洲区立才学校2023-2024学年八年级上学期月考数学试题(已下线)猜想06 平行线的证明和三角形内角和定理(易错必刷36题9种题型)-2023-2024学年八年级数学上学期期末考点大串讲(北师大版)辽宁省营口市大石桥市八校2023-2024学年八年级上学期12月考试数学试题(已下线)专题02 三角形全等的性质与判定、角平分线之八大题型-【好题汇编】备战2023-2024学年八年级数学上学期期末真题分类汇编(人教版)山东省德州市宁津县第一实验中学2023-2024学年八年级上学期10月月考数学试题(已下线)专题04 全等三角形培优综合专项训练(旋转模型)-【好题汇编】备战2023-2024学年八年级数学上学期期末真题分类汇编(广东专用)(已下线)专题10 平行线的证明(七种考法)-【好题汇编】备战2023-2024学年八年级数学上学期期末真题分类汇编(北师大版)(已下线)清单03 全等三角形经典模型(9种题型解读(40题))-2023-2024学年八年级数学上学期期末考点大串讲(苏科版)
7 . 如图,在
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/778cee0c-4a80-40ff-aeb0-1e12a5dc311a.png?resizew=243)
(1)请用直尺和圆规,作出
边的垂直平分线
,交
于点
,交
于点
,连接
:(只保留作图痕迹)
(2)求
的度数.
解:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f945fdf3cf03f1921c33151aac7849c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf284258bd221bef93395fe896b47e0.png)
①______
垂直平分![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4c31d03909bc82980aa9dbbaaf1a2f.png)
③______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398511d6449a07997879e6fae3579d95.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/778cee0c-4a80-40ff-aeb0-1e12a5dc311a.png?resizew=243)
(1)请用直尺和圆规,作出
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5157b42da58d55daad27d98b2fec15ff.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f945fdf3cf03f1921c33151aac7849c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf284258bd221bef93395fe896b47e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897148e18b15466a7b3fb87fb886845b.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/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4c31d03909bc82980aa9dbbaaf1a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/401814fb1e410facefbf16c12a880efe.png)
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名校
8 . 已知:如图,在
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/26/a915f72b-760c-45a2-a403-b2410f095e0c.png?resizew=180)
(1)尺规作图:作
的垂直平分线
分别与
、
交于点
、
;
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/26/a915f72b-760c-45a2-a403-b2410f095e0c.png?resizew=180)
(1)尺规作图:作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
9 . 如图,矩形
中,
,分别以点
,
为圆心,大于
的长为半径画弧,两弧交于点
、
,直线
分别交
、
于点
、
.若
,
,则四边形
面积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/4469e1a3-ad57-4d14-a6ea-039d32230f5e.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6694f3443cc5f4d09948679251b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93148adbc6e856da9a9d263f485d003.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/411461db15ee8086332c531e086c40c7.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9766e5eb6796dafc5ffe212afdfc43c0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/4469e1a3-ad57-4d14-a6ea-039d32230f5e.png?resizew=168)
A.20 | B.16 | C.12 | D.24 |
您最近一年使用:0次
10 . 如图,含30°的三角板ABC,
,
,
,把三角板ABC绕点A旋转,点B、C的对应点分别为
、
,若
的一边与
的一边重合(不含与
一边的延长线重合的情况),连接
,则
的值为__________ .
![](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/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc9076974ebd6331d67055302be8167.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/400fe469-1ebb-4d18-9505-a630b173798c.png?resizew=184)
您最近一年使用:0次