1 . 如图,四边形
为正方形,且
是边
延长线上一点,过点
作
于
点,交
于
点,交
于
点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/1537ce82-faaf-49ef-b40c-de2cd2d45274.jpg?resizew=159)
(1)求证:
;
(2)求证:
;
(3)连接
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7a3dc3f3a02f4400e22dec2f2fee23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/1537ce82-faaf-49ef-b40c-de2cd2d45274.jpg?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c5b1f09304e13bf30161a3069a3a2f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c9d29818f14596a0ecd7d412d47cc6.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfe3f2c19beb2513f3b27b764d98094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7d1a478f313c3280060ab38cc8b9e2.png)
您最近一年使用:0次
名校
2 . 江老师有一天为了测量一棵高不可攀的银杏树高度,他利用了反射定律,利用一面镜子和皮尺,设计如图所示的测量方案:把镜子放在离银杏树
的点
处,然后观测者沿着直线
后退到点
,这时恰好在镜子里看到树梢顶点
,再用皮尺量得
,观测者目高
,则树高
约是多少
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1edf37c104d215fed83a125f88b651d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734ac463c26fa5caea9e4846bbe53d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be62f0ad93c5c6605a053230233ae47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
您最近一年使用:0次
2023-12-29更新
|
184次组卷
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9卷引用:湖南省株洲市渌口区2023-2024学年九年级上学期期末数学试题
湖南省株洲市渌口区2023-2024学年九年级上学期期末数学试题湖南省长沙市开福区青竹湖湘一外国语学校2020-2021学年九年级上学期期中数学试题新疆维吾尔自治区乌鲁木齐市第九中学2023-2024学年九年级下学期期末数学试题(已下线)第14讲 相似三角形的性质及应用—【帮课堂】2022-2023学年九年级数学上册同步精品讲义(北师大版)(已下线)专题4.23 利用相似三角形测高(专项练习)-2022-2023学年九年级数学上册基础知识专项讲练(北师大版)(已下线)专题15利用相似三角形测高(3个知识点2种题型1种中考考法)-【帮课堂】2023-2024学年九年级数学上册同步学与练(北师大版)(已下线)第4章 图形的相似(单元测试·基础卷)-2023-2024学年九年级数学上册基础知识专项突破讲与练(北师大版)江西省萍乡市安源中学2023-2024学年九年级上学期月考数学试题(已下线)2024年江苏省连云港市中考数学真题变式题22-27题
3 . 如图,A,B两点被池塘隔开,小吴为了测量A,B两点间的距离,他在
外选一点
,连接
和
,延长
到
,延长
到
,
,连接
,使
.若小吴测得
的长为
米,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
______ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8455657dde27aabe6adb7b188e031c11.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/7efc841d4bd475c8f9f8ce2d682d783b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066cd386723885c535ea720f5817847a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b685c556cc423e4833c1dc671a134cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/214e31b4-c2e8-406a-a9d1-a94b883077e2.png?resizew=128)
您最近一年使用:0次
2023-12-26更新
|
62次组卷
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3卷引用:湖南省长沙市立信中学2023-2024学年九年级上学期期末数学试题
名校
4 . 如图,在
中,
,
于点
,
,
,则
的长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/06f0e5e2-394f-429b-a2b0-e9d66ffb057f.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/06f0e5e2-394f-429b-a2b0-e9d66ffb057f.png?resizew=163)
A.3 | B.4 | C.5 | D.6 |
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2023-12-20更新
|
145次组卷
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3卷引用:湖南省衡阳市耒阳市广湘初级中学2023-2024学年九年级上学期期末数学试题
23-24九年级上·湖南长沙·期末
5 . 如图,在
中,
,
,点
在
的延长线上,且
,过点
作直线
分别交边
,
于点
,
.若直线
将
的面积平分,则线段
的长为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](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/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/24570630-d242-49c2-92a9-af0d1b29c967.png?resizew=224)
您最近一年使用:0次
6 . 如图,在
中,
,
,
的面积是8,则四边形
的面积是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c436f108fd4921dae15ecff19270237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c0a8e2f1847f9d78ad367d8ee8ae10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce735bef8c7fc6a1ddcebd449e38f7e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/c11c43cf-7ead-438b-9589-c938611777d1.png?resizew=141)
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2023-12-15更新
|
124次组卷
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2卷引用:湖南省永州市双牌县阳明学校2022-2023学年九年级上学期期末数学试题
名校
7 . 如图,
的直角顶点
与坐标原点重合,
,若
点在反比例函数
的图象上,则过
点的反比例函数的比例系数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/cec1c3da-2a4d-40aa-b8e4-6c93998ef76c.png?resizew=155)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c633830c6e2ac6d8d6e18890ef5ee33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1df17440481c8da8e0a17f008dbc4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ff6ca15946b9c0b2e5ebaf9eff533c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/cec1c3da-2a4d-40aa-b8e4-6c93998ef76c.png?resizew=155)
A.2 | B.4 | C.![]() | D.![]() |
您最近一年使用:0次
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3卷引用:湖南省岳阳市岳阳县2023-2024学年九年级上学期期末数学试题
湖南省岳阳市岳阳县2023-2024学年九年级上学期期末数学试题河北省石家庄市第九中学2023-2024学年九年级上学期期中数学试题(已下线)寒假作业12 反比例函数的基本模型-【寒假分层作业】2024年九年级数学寒假培优练(人教版)
8 . 如图,直线
与反比例函数
交于点B,与x轴和y轴分别交于点A和点D,
于点C,若点D是线段
的中点,
,
,则k的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8182ab03bccb2d62d2941d94c339093c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
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2023-12-11更新
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5卷引用:湖南省怀化市八县九校联合调研考试2023-2024学年九年级上学期期末数学试题
湖南省怀化市八县九校联合调研考试2023-2024学年九年级上学期期末数学试题山东省东营市垦利区2023-2024学年九年级上学期期中数学试题山东省烟台市莱州市2023-2024学年九年级上学期期中数学试题2024年辽宁省铁岭市开原九年级中考一模后数学模拟预测题(已下线)第02讲 反比例函数的图像与性质的综合应用-【帮课堂】2023-2024学年九年级数学下册同步学与练(人教版)
9 . 【问题情境】
如图1,小明把三角板
(
)放置到矩形
中,使得顶点E、F、G分别落在
、
、
上,你发现线段
与
有什么数量关系?
直接写出结论:______(不用证明).
【变式探究】
如图2,小明把三角板
(
)放置到矩形
中,使得顶点E、F、G分别在
边上,若
,
,求
的长.
【拓展应用】
如图3,小明把三角形
放置到平行四边形
中,使得顶点E、F、G分别落在
边上,若
,
,
,求出
的值.
如图1,小明把三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd82f3c96014272fa70e863b18ea67d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
直接写出结论:______(不用证明).
【变式探究】
如图2,小明把三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd82f3c96014272fa70e863b18ea67d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ae59eba8716379c96c35dcd4bac63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a6b99b747b14ab29c30e3ff4838057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb6823a329628699619a39cde927510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
【拓展应用】
如图3,小明把三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ae59eba8716379c96c35dcd4bac63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67f75b7637f0f2b428160004485d682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bfef1acfd3661e518473fb1ef246fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa421e8c88be98a527d2a6f04981e602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49b962754b4797294f22ca3d2e57eec.png)
您最近一年使用:0次
2023-12-06更新
|
78次组卷
|
2卷引用:湖南省岳阳市2023-2024学年九年级上学期期末数学试题
10 . 如图,在
中,点E在
上,
,
和
相交于点F,过点F作
,交
于点G.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/3aada9fe-0e77-4822-9962-4e7bf7728b7a.png?resizew=177)
(1)求
的值.
(2)若
,
①求证:
.
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275d68d50a992cb17d948d3299012a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad73a486121bb421284c7c3ab1a69f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/3aada9fe-0e77-4822-9962-4e7bf7728b7a.png?resizew=177)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca07b4b1d1d30ebf0a5a402ad8aeecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a336aa4070bd9dbd439c16723ed44457.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68229092cd780e5a310e505ec6fb0897.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d0448d5ba254ab79b9f2c6be1f904a.png)
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2023-11-30更新
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135次组卷
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2卷引用:湖南省长沙市长郡教育集团联考2023-2024学年九年级上学期期末数学试题