1 . 凸透镜成像的原理如图所示,
.若焦点
到物体的距离与焦点
到凸透镜中心线
的距离之比为
,则物体被缩小到原来的__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160100c9dd30ec7cafa1d579ced7045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84783b6ba0f36789519816101a437f46.png)
您最近一年使用:0次
2 . 综合与实践
折纸中蕴藏着丰富的数学知识,也启迪着数学问题的解决.综合实践课上,老师和同学们一起通过折纸,探究数学的奥秘.
如图1,在矩形纸片
中,点
、
分别在边
和
上,将矩形纸片
沿
折叠,点
落在
边上的点
处,点
落在点
处,连接
,则
与
的位置关系为______;
折叠一:小明发现,当点
和点
重合时,连接
,如图2,则有
,请说明理由;
折叠二:如图3,若矩形
是一张A4纸
,探究
、
和
三者之间的数量关系,并说明理由;
【解决问题】
小华受【折纸探究】的启发,解决了下面的问题.
如图4,在矩形纸片
中,点
、
分别在边
和
上,连接
、
、
,
平分
,
,
,求
的值.(用含有
的代数式表示)
折纸中蕴藏着丰富的数学知识,也启迪着数学问题的解决.综合实践课上,老师和同学们一起通过折纸,探究数学的奥秘.
如图1,在矩形纸片
![](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/a0ed1ec316bc54c37c4286c208f55667.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
折叠一:小明发现,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc72dcea754dff2adbcb0813051f4625.png)
折叠二:如图3,若矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18cb93f2eb017d894c8f1bd9240734b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
【解决问题】
小华受【折纸探究】的启发,解决了下面的问题.
如图4,在矩形纸片
![](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/a0ed1ec316bc54c37c4286c208f55667.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6a23d521606a35298bbf147f7f830c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d96a5d40d0aea9f4398ca4d0fe9b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d042670d1b964f57f9d636b8a5ff51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a4c86103260c233b26ec7dc50ad1ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
3 . 如图1,
内接于⊙O,
,D为
上一点,
交
延长线于点E.
为
的切线;
(2)如图2,连接
恰好过圆心,过点A作
于G,过点C作
于F.
①求证:
;
②若
,求
的长.
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542b5bc10c7341c04c22244f3ec16e6a.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/3d97cdc586744d208b6f69c9813af977.png)
(2)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823b421ffc231eaa1e6dd9d3e6ef169b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bad3d9422cf9c0b078900b3c507e87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac18b0388014ae20b2add2975ef56aa.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef7b745016d59c0edb26bc64c4f5f8b.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76839a80ac2e7fc7a52055528b77fd3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
4 . 如图1,已知点
,
,反比例函数
与直线AB有唯一一个交点.
,
时,求直线
的解析式及k的值;
(2)当
的面积为10时,求k的值;
(3)当
,且k的最大值为9时,将此时的直线
沿着x轴正半轴方向移动,交反比例函数
于点C、D(如图2),若点C是线段
的中点,求平移的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b9486ec9dca95979803bf91ca6c337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db91b4d5741dd21b9615ced9c76fd507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a8b6fe6b9add4a965ac32c1fc51c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab04de6651256f6281e9f4c1dc3c7955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72592a024429055d4ad4b369f025cd3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
5 . 【数学眼光】
星港学校比邻园区海关大楼,星港学校九年级学生小星在学习过“相似”的内容后,也想要利用相似的知识得海关大楼的高度,如图1所示.小星选择把数学和物理知识相结合利用平面镜的镜面反射特点来构造相似,如图2所示.
问题一:现测量得到
,
,
.问:海关大楼高
高为多少?(用
,
,
表示)
【数学思维】
但在进一步观察海关大楼周围的环境之后,小星发现由于条件限制,海关大楼的底部不可到达,所以无法准确测量海关大楼底部到平面镜的距离,如图3所示,在老师帮助下小星进一步完善了自己的想法,得到了方案二:既然无法测量平面镜到海关大楼底部的距离,那就将这部分用其他长度来表示,即构造二次相似,将测量距离进行转化,如图4所示.
,
,
,
,请你求出海关大楼
的高度.
【数学语言】
问题三:小星在求出来数据之后,上网查阅了资料发现海关大楼高度为
,请你尝试着分析出现这样误差的原因是什么?
星港学校比邻园区海关大楼,星港学校九年级学生小星在学习过“相似”的内容后,也想要利用相似的知识得海关大楼的高度,如图1所示.小星选择把数学和物理知识相结合利用平面镜的镜面反射特点来构造相似,如图2所示.
问题一:现测量得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d57dfe6b153c88751ff8bfd2809df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd764314ae7afde76f32918f79ccc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
【数学思维】
但在进一步观察海关大楼周围的环境之后,小星发现由于条件限制,海关大楼的底部不可到达,所以无法准确测量海关大楼底部到平面镜的距离,如图3所示,在老师帮助下小星进一步完善了自己的想法,得到了方案二:既然无法测量平面镜到海关大楼底部的距离,那就将这部分用其他长度来表示,即构造二次相似,将测量距离进行转化,如图4所示.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4680162737e2b843348c3c3ce92e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5444ed21f3b963c65fbbc26ee819f0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8523cf93057cdbb73c80b179b31da9da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f69fab139bf9cc09e3daa34b34417a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
【数学语言】
问题三:小星在求出来数据之后,上网查阅了资料发现海关大楼高度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b90845b89ff1044579e647c1f1cc56e.png)
您最近一年使用:0次
名校
6 . 如图①,
为
的直径,弦
交
于
(点
不与点
,
重合),连结
,
.
;
(2)如图②,若
,求证:
;
(3)在(2)的条件下,若
,直接写出
的值_________;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc39ef7111e12f74d3843a0cf84944c.png)
(2)如图②,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1dff2e124de97afa94697a8e29f642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7347a16b5d4850a915c8691f2924a87e.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0786d9296cf341317c2a830706f56380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ff5fcad35756d6bc7b2baa9068ad63.png)
您最近一年使用:0次
7 . 如图,P为⊙O的直径
延长线上的一点,
为⊙O的切线,切点为C,
于D,连接
.
平分
;
(2)若
,
,求⊙O的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.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/76d221944148d71e2e1bc76040aefb8d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd941979247e370b47de36639d798af.png)
您最近一年使用:0次
2024-06-14更新
|
231次组卷
|
3卷引用:2024年江苏省盐城市亭湖区等2地中考二模数学试题
名校
解题方法
8 . 如图,等边
的边长为3,点D在边
上,
,线段
在边
上运动,
,有下列结论:①
与
可能相等;②
与
可能相似;③四边形
面积的最大值为
;④四边形
周长的最小值为
,其中,正确结论的序号为_______ .
![](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/9ffbcd82b98a9ae69aa4ee28bb49a907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145ae2355fd8310654760e2fe0bee87f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c118858379800688c993a8b61270b356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe7a785ff74d9aa4027bec2cdc06513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3dac3f1a7727e2b848e5881a03a8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89339a61df708313d12750d9741b43a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3dac3f1a7727e2b848e5881a03a8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d278f7b4f402ed6ace159a518b1565.png)
您最近一年使用:0次
2024-06-13更新
|
46次组卷
|
2卷引用:2024年江苏省苏州市高新区九年级中考第二次模拟数学试题
9 . 如图,在矩形
中,点E、F是对角线
上的两点,
,
,点G是边
的中点.当
取最小值时,
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45723dce96b74f027adcb1a4ecd19db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d163ba9cef35eb600387bcfbbda89ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e997f1bcb6549e664327b02a8a8e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbbf9d5bd000c50029bda34070ed0b6.png)
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10 . 如图,
是
的外接圆,
是
延长线上一点,且
平分
的平分线与
分别交于点
.
;
(2)求证
;
(3)若
,则
______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a6f0000fa1dd6c72ff0f41e48e2540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682955cb8bf89737f148e056702b9b19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92dbe7d01d47d6c2db1396180caf76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d603566c74b1d5de510a2e8f7859010.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d6e3eb9ab6b8e25abec286eaca3deb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a99b815e51e22f3f7b2e01b42cbe099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524f25e1eedbfe399f7f42db890ab89a.png)
您最近一年使用:0次