1 . 下列说法中正确的是( )
A.两条直线被一组平行线所截,所得的线段成比例 |
B.对于反比例函数![]() |
C.关于x的方程 ![]() |
D.正方形的每一条对角线平分一组对角 |
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2 . 如图,在中,
,
,
,点D为AB上一点,且
,点E为AC上一动点,连接ED,过点D作
,交直线BC于点F,点G为EF的中点,当点E从点A运动到点C,点G的运动路径长为
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3 . 综合与探究:如图1,已知抛物线
与
轴相交于
,
两点(点
在点
的左侧),与
轴相交于点
,直线
与
轴相交于点
,交线段
于点
,且
.
,
,
三点的坐标;
(2)求直线
的函数表达式;
(3)如图2,若抛物线的对称轴
与直线
交于点
,试探究,在平面内是否存在一点
,使以点
,
,
,
为顶点的四边形为平行四边形.若存在,求出点
的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0f24bb0de4944ac3f4723ec488cf51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/f594f063df440c265a6c0adb51fbeb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)如图2,若抛物线的对称轴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/acc290b44635265137fdf13146b6a6d9.png)
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4 . 如图,在
中,
,按以下步骤作图:①分别以点
和点
为圆心,大于
的长为半径作弧,两弧相交于
,
两点;②作直线
交
于点
,连接
.若
,则
的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a05e0ab55e325fb3b85fc8ca9c27c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
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5 . 【问题初探】
在数学活动课上,张老师给出如下问题:“如图1,在
中,
是
的角平分线,求证:
”,有两名同学给出了不同的解答思路:
①如图2,小丽同学从结论出发给出如下解题思路:过点C作
的平行线交
的延长线于点E,运用等腰三角形和相似等知识解决问题.
②如图3,小强同学从“
是
的角平分线”给出了另一种解题思路:在
上截取
,连接
,过点C作
的平行线交
的延长线于点G,也是利用相似等知识解决问题.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/23/24e09359-b691-4104-9351-fe58c061b6b3.png?resizew=817)
(1)请你选择一名同学的解答思路,写出证明过程.
【类比分析】
张老师发现之前两名同学都运用了转化思想,将两组线段比值问题转化为两三角形相似的对应边的比.为了帮助学生更好地领悟这种转化思想,张老师将问题进行了改编,提出下面问题,请你解答.
(2)如图4,若
的外角
平分线
交
的延长线于点D,求证:
.
【学以致用】
(3)如图5,在四边形
中,
,
,
,
平分
,求
的长.
在数学活动课上,张老师给出如下问题:“如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5ca418ff0d36929cd06551f74d58c2.png)
①如图2,小丽同学从结论出发给出如下解题思路:过点C作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
②如图3,小强同学从“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14833dbeed409b33acd4c9071fd0be36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/23/24e09359-b691-4104-9351-fe58c061b6b3.png?resizew=817)
(1)请你选择一名同学的解答思路,写出证明过程.
【类比分析】
张老师发现之前两名同学都运用了转化思想,将两组线段比值问题转化为两三角形相似的对应边的比.为了帮助学生更好地领悟这种转化思想,张老师将问题进行了改编,提出下面问题,请你解答.
(2)如图4,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b40c2b0ab8e1cfe5112d428b4b829f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35803969509655f72b4118503ae1c966.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/ea5ca418ff0d36929cd06551f74d58c2.png)
【学以致用】
(3)如图5,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2ee4d985e634e127a8db9fae7ab837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881eed6c1283ad910459a665fe3ee395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
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6 . 在
中,
,
平分
交
于点
交
于点
,
交
于点
,有以下结论:①四边形
一定是平行四边形;②连接
所得四边形
一定是平行四边形;③保持
的大小不变,改变
的长度可使
成立;④保持
的长度不变,改变
的大小可使
成立,其中所有的正确结论是:________ .(填序号即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.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/a4a45d141f3e1e3f46ddc63fdc5ce68c.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/18574218da07c7acb52275b2a29d941b.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/2222eec085423ac1c57089962f3287f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bdae3d30abf70515bdbd45f9d0c380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c114237f609956017bc72f4971d5b375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c114237f609956017bc72f4971d5b375.png)
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2024-03-22更新
|
193次组卷
|
3卷引用: 江苏省泰州中学附属初级中学2023-2024学年八年级下学期3月月考数学试题
7 . 如图,装有某种液体的工业用桶中放置有一根搅拌棍.工人师傅为了解桶内所装液体的体积,先在搅拌棍所处桶孔位置做好标记点A,并取出;然后测得搅拌棍接触到液体部分
m,搅拌棍A到底端D处的长度为
,最后测量出桶的高
为
,圆桶内壁的底面直径为
.已知桶内的液面与桶底面平行,其平面示意图如图2所示.请你根据以上数据,帮工人师傅计算出桶内所装液体的体积(结果保留π)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb08f6a798dc293f3d8de281190f65e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863857a5d6eb825523ce5e4720537be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d8fef97b2674915e3c690bc69d6614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0bb863aba7910e3ba8452a2c29b347.png)
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8 . 一个矩形
按如图
的方式分割成三个直角三角形,把较大的两个三角形纸片按图
方式放置,若图
中两个阴影部分面积满足
,下列结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3527e8ebadab9bf9de07f7a9818e77c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 如图,已知等边,D是边
的中点,过D作
于E,连接
交
于
;过
作
于点
,连接
交
于
;过
作
于
,…如此继续,若记
为
,记
为S₂,记
为S₃…,若
面积为
,则
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10 . 如图的网格中,
的顶点都在格点上,每个小正方形的边长均为1.仅用无刻度的直尺在给定的网格图中分别按下列要求画图.(保留画图痕迹,画图过程中辅助线用虚线,画图结果用实线、实心点表示)
的高
.
(2)请在图2中在线段
上找一点E,使
.
![](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/d40b319212a7e7528b053e1c7097e966.png)
(2)请在图2中在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86338536656046e93b53672ade9a78b3.png)
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2024-03-19更新
|
400次组卷
|
9卷引用:2024年浙江省温州市外国语学校中考一模数学试题
2024年浙江省温州市外国语学校中考一模数学试题浙江省杭州市西湖区十三中教育集团(总校)2023-2024学年九年级下学期4月月考数学试题(已下线)专题08 几何作图问题1-2024年中考数学二轮热点题型归纳与变式演练(江苏专用)2024年甘肃省武威四中联片教研九年级第三次模拟数学试题2024年甘肃省武威市民勤县民勤六中教研联片九年级中考三模数学试题(已下线)抢分通关05 几何作图问题(含无刻度作图,2易错12题型)-备战2024年中考数学抢分秘籍(全国通用)2024年甘肃省武威市天祝藏族自治县天祝县民族中学联片教研中考三模数学试题2024年甘肃省武威十三中片区考九年级中考数学三模试题2024年甘肃省金昌市永昌县第五中学联片教研中考三模数学试题