1 . 某数学学习小组学习完四边形后进行了如下探究,已知四边形
为矩形,请你帮助他们解决下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/bffe69d3-dcf4-4aa1-9fe7-908c21d2a5e0.png?resizew=447)
(1)【初步尝试】:他们将矩形
的顶点
、
分别在如图(1)所示的
的边
、
上,顶点
、
恰好落在
的对角线
上,求证:
;
(2)【深入探究】:如图2,若
为菱形,
,若
,求
的值;
(3)【拓展延伸】:如图(3),若
为矩形,
;
且
,请直接写出此时
的值是________(用含有
,
的代数式表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/bffe69d3-dcf4-4aa1-9fe7-908c21d2a5e0.png?resizew=447)
(1)【初步尝试】:他们将矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f90a3773e6944013a0eb41279f332f.png)
(2)【深入探究】:如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a3ae16e3f4a6b8994eb716f8502ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e9fe9bcc967fb43ea66ab995f7c1c9.png)
(3)【拓展延伸】:如图(3),若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3be96420ac78c8621fcb47a45514fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7be5da220f32cb7c8aad9ca5ced32e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a3ae16e3f4a6b8994eb716f8502ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01943be6d886ec97fc1c18e73b0d4ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2024-01-18更新
|
155次组卷
|
3卷引用:广东省深圳市南山区2023-2024学年九年级上学期期末数学试题
2 . (1)问题背景
如图1,
中,
,
,
的平分线交直线
于
,过点
作
,交直线
于
.请探究线段
与
的数量关系.(事实上,我们可以延长
与直线
相交,通过三角形的全等等知识解决问题.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
结论:线段
与
的数量关系是 (请直接写出结论);
(2)类比探索
在(1)中,如果把
改为
的外角
的平分线,其他条件均不变(如图
,(1)中的结论还成立吗?若成立,请写出证明过程;若不成立,请说明理由;
(3)拓展延伸
在(2)中,如果
,且
,其他条件均不变(如图
,请你直接写出
与
的数量关系.
结论:
(用含n的代数式表示).
如图1,
![](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/047dc9795efa99b6fb9fdf9778085dab.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45b04cc3e5adaeff6f9e01e29032803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
结论:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)类比探索
在(1)中,如果把
![](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/3d786ee723231d4ca87eb9d011a378b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad217e26bd3580c35998109de14cef73.png)
(3)拓展延伸
在(2)中,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6eab933fd3ed8a3a412a6f268d4cef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d68c94069d6f8f2f7b11fe83f7acd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2324a65e345753fdd1db2354bfb0ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
结论:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/937e0197-6e18-41b6-a0f3-7d0c678b0072.png?resizew=426)
您最近一年使用:0次
3 . 图形的旋转变换是研究数学相关问题的重要手段之一,小华和小芳对等腰直角三角形的旋转变换进行了研究.如图(1),
和
均为等腰直角三角形,点
,
分别在线段
,
上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1bff74f3356bff74a51c48524bd13b.png)
绕点
逆时针旋转,连接
,
,如图(2),当
的延长线恰好经过点
时,其:
①
的值;
②
与
的夹角为多少度;
(2)类比探究:如图(3),小芳在小华的基础上,继续旋转
,连接
,
,设
的延长线交
于点
,(1)中的两个结论是否仍然成立?请说明理由.
(3)拓展延伸:若
,
,当
所在的直线垂直于
时,请你直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0e1bff74f3356bff74a51c48524bd13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9af91834644b94e1b023b33e15a0644.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)类比探究:如图(3),小芳在小华的基础上,继续旋转
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)拓展延伸:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e50f0d02d0bd51ae361d276ed9dea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9f93c7e7f4b9244cc5c6cc4dece9d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
4 . (1)【探究发现】如图①,已知四边形
是正方形,点E为
边上一点(不与端点重合),连接
,作点D关于
的对称点
,
的延长线与
的延长线交于点F,连接
,
.
①小明探究发现:当点E在
上移动时,
,并给出如下不完整的证明过程,请帮他补充完整.证明:延长
交
于点
.
②进一步探究发现,当点
与点F重合时,
___________
.
(2)【类比迁移】如图②,四边形
为矩形,点
为
边上一点,连接
,作点D关于
的对称点
,
的延长线与BC的延长线交于点F,连接
,
,
,当
,
,
时,求
的长;
(3)【拓展应用】如图③,已知四边形
为菱形,
,
,点F为线段
上一动点,将线段
绕点A按顺时针方向旋转,当点D旋转后的对应点E落在菱形的边上(顶点除外)时,如果
,请直接写出此时
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b25f3ea33cc08b1e2a0d9c3a9dccaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f611f5bb08a66cae8fe411e59a1c08e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/2853ec4b-cc3f-4f92-9b69-b5c7cec18a53.png?resizew=532)
①小明探究发现:当点E在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32577dda778c0bd267c4ece7bfcacf76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
②进一步探究发现,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b6d0cf1c51302804d95d715178a7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
(2)【类比迁移】如图②,四边形
![](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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b25f3ea33cc08b1e2a0d9c3a9dccaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ba89e83329983cfadbfcdda151aaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f611f5bb08a66cae8fe411e59a1c08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46562e866eb760487b101c250328335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ba89e83329983cfadbfcdda151aaa3.png)
(3)【拓展应用】如图③,已知四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ce838f38419e8781d63b3417cac5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
您最近一年使用:0次
5 . 【问题提出】
如图1,在正方形
中,点E,F分别在
边上,且
,连接
.探究线段
之间的数量关系.
【方法感悟】
(1)小明组同学利用构造全等三角形的方法探究三条线段的关系:如图2,延长
到点G,使
,连接
,先证明
,再证明
,从而得到正确结论.小明组同学的结论是___________;
小亮组同学对小明组构造全等三角形的环节提出了不同的看法,借助旋转三角形的方式探究问题:将
绕点A顺时针旋转90°得到
,再证明
,从而得到与小明组相同的结论.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/4194d793-1550-4e2e-aa10-0f8a33d87114.png?resizew=302)
【方法迁移】
(2)如图3,在
中,
,沿边
翻折得到
,点B的对应点为点D,点E,F分别在
边上,且
.试猜想线段
之间的数量关系,并证明你的猜想.
【问题拓展】
(3)如图4,在四边形ABCD中,
,点E,F分别在
边上,且
,试猜想当
与
满足什么关系时,可使得
.请直接写出你的猜想.
(4)如图5,在四边形
中,
,
,
与
为对角线,
.若
,
,求
的长.
如图1,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ced9844fe2e052c70486af0740afa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192155e6a3aade305b76b1eb7c75e30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180942edc839b9fda741b055df87216b.png)
【方法感悟】
(1)小明组同学利用构造全等三角形的方法探究三条线段的关系:如图2,延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b555a0bb6b5132ecfb9cae3769912c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828d0ee008783093cbe6de3f5147bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7d143a1d6ba708f17021e41efd7d9a.png)
小亮组同学对小明组构造全等三角形的环节提出了不同的看法,借助旋转三角形的方式探究问题:将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc727c642cbc2181476b7dd8eca471e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7d143a1d6ba708f17021e41efd7d9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/4194d793-1550-4e2e-aa10-0f8a33d87114.png?resizew=302)
【方法迁移】
(2)如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ced9844fe2e052c70486af0740afa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6aef04eceb608a7a2cfc3e566f9e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180942edc839b9fda741b055df87216b.png)
【问题拓展】
(3)如图4,在四边形ABCD中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ced9844fe2e052c70486af0740afa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6aef04eceb608a7a2cfc3e566f9e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c543c3ddc3723fde6bbfca3ea3b921b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a99627df7b1a88b9bf3dda20390d245.png)
(4)如图5,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7305de9211785b826823153897b17517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669f7a1e43ef893ef3a45fc47992947f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2915ea6f8ea0cb67a6b135ff275b4e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/7872072e-8e14-41b4-88ca-a0923e1c29d7.png?resizew=459)
您最近一年使用:0次
2024-01-10更新
|
390次组卷
|
3卷引用:辽宁省沈阳市于洪区2023-2024学年九年级上学期期末数学试题
6 . 综合与实践
问题情境:
中,
,
,
于点D,点E是射线
上的一个动点(不与点A重合)将线段
绕点A顺时针旋转
得到线段
,连接
交线段
于点G.交
于点H、连接
.
特例分析:
(1)如图1,当点E与点D重合时,“智敏”小组提出如下问题,请你解答:用等式表示线段
与
之间的数量关系为:_______;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/72ab4383-8f68-4c12-8296-8e797bf8e6cc.png?resizew=157)
拓展探究:
(2)如图2,当点E在线段
的延长线上,且
时,“博睿”小组发现
.请你证明;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/1d4e2e08-dcfb-4407-b7ee-4b00f5a3133b.png?resizew=156)
(3)如图3,当点E在线段
的延长线上,且
时,
的值为_______;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/265f01df-d2b0-4912-b638-85af79fedb3f.png?resizew=162)
推广应用:
(4)当点E在射线
上运动时,
,则
的值为_______(用含m,n的式子表示).
问题情境:
![](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/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
特例分析:
(1)如图1,当点E与点D重合时,“智敏”小组提出如下问题,请你解答:用等式表示线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/72ab4383-8f68-4c12-8296-8e797bf8e6cc.png?resizew=157)
拓展探究:
(2)如图2,当点E在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad98ad714864041a632ca949308e417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850c12524ad7df9aa5ed4f02cd603e40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/1d4e2e08-dcfb-4407-b7ee-4b00f5a3133b.png?resizew=156)
(3)如图3,当点E在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5fc6ead6416492c231c320a5486f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae2e8b074cb592effa45491c94d07f4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/265f01df-d2b0-4912-b638-85af79fedb3f.png?resizew=162)
推广应用:
(4)当点E在射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbe02327b24c37218035da7939b7360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae2e8b074cb592effa45491c94d07f4.png)
您最近一年使用:0次
名校
7 . 操作初探:
(1)如图1,将正方形纸片
对折,使
与
重合,展平纸片,得到折痕
;再对折,使
与
重合,得到折痕
,展平纸片,连接
,与
交于点
,连接
,
.则
的值为________;
猜想证明:
(2)如图2,将正方形纸片
对折,使
与
重合,展平纸片,得到折痕
;点
在
边上,连接
,与
交于点
,连接
,将
绕点
逆时针旋转,使点
的对应点
'落在对角线
上,连接
.当点
在边
上运动时(点
不与
,
重合),试判断
的形状,并说明理由.
拓展探究:
(3)如图3,在(2)的条件下,延长
交
于点
,连接
,
.当
平分
时,请证明
.
(1)如图1,将正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafbe2751f4f4c5a8e676818195e9111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7ea03277f8408fabe5b327cc34838f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365822bd3945e6a3e871ca979c84cc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f1f15f0de2b8b8da87056362fbea5a.png)
猜想证明:
(2)如图2,将正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bc9983f123701604ea131508334e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed9ac5ae3774f97db118b790aab46ba.png)
拓展探究:
(3)如图3,在(2)的条件下,延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365822bd3945e6a3e871ca979c84cc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365822bd3945e6a3e871ca979c84cc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63005a1a1f37e4d90369d71d4f91d2a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd54f390e1c87bff710879a4a31ca93b.png)
您最近一年使用:0次
今日更新
|
53次组卷
|
2卷引用:2024年陕西省西安市雁塔区陕西师范大学附属中学中考九模数学试题
名校
8 . 已知
的半径为5,
是长为8的弦,
于点
,点
在
的延长线上,且
. 弦
从图1的位置开始绕点
逆时针旋转,在旋转过程中始终保持
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/a7b6bb9e-d08a-4e87-9f0d-f61e280371b9.png?resizew=436)
[发现] 在旋转过程中,
(1)
的最小值是__________,最大值是__________.
(2)当
时,旋转角
__________.
[探究] 若
绕点
逆时针旋转
,如图3,求
的长.
[拓展] 如图4,当
切
于点
交
于点
于
.
(1)求
的长.
(2)此时
__________,
__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589d71492157e7690492c8ace7092eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59faf75f0c95312e556ae905b3ff5b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5362227d4f7d22791604fa66a3385e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589d71492157e7690492c8ace7092eb7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/a7b6bb9e-d08a-4e87-9f0d-f61e280371b9.png?resizew=436)
[发现] 在旋转过程中,
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790f772a9bdbfd9fa4e7a20438341b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
[探究] 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
[拓展] 如图4,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b763b64697ce52d8fcd9102dd7ccd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90c780dac29ff8b7df5881d3b33abab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925fef214857e010e2b0ef1466c8c56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)此时
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3943224ebad9517a0611e0a0b039952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7a5de06d5577a27967d000e360e851.png)
您最近一年使用:0次
9 . 【探究发现】
(1)如图(a),正方形
的边长为6,E为边
的中点,F是边
上的一点,将
沿
对折,点B的对应点为点G,当点G恰好落在
上时,求
的长.
(2)如图(b),E,F分别是矩形
的边
,
上的点,
,
,F为
的中点,将
沿
对折,点B的对应点为点G.连接
,当
时,求四边形
的面积.
(3)菱形
的边长为6,
,E是边
上一点,F是边
上一点,将
沿
对折,点B的对应点为点G.当点G落在菱形的一条边或一条对角线上,且
时,直接写出BF的长度.
(1)如图(a),正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)如图(b),E,F分别是矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60634341a9603e24b2bbc6960abe3d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68edd1a8e6746d55b632f78552e0540.png)
(3)菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.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/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6cee83d36c4da913e0790e5070c46f.png)
您最近一年使用:0次
10 . 综合与实践
教材重现:取一块质地均匀的三角形木板,用一枚铁钉顶在这个三角形的重心上,木板会保持平衡(如图),这是重心的物理性质.
,如图,
,
.为了找到重心,以便像教材上那样稳稳用笔尖顶起,她先把点
与点
重叠对折,得折痕
,展开后,她把点
与点
重叠对折,得折痕
,再展开后连接
,交折痕
于点
,则点
就是
的重心.
,判断
与
的数量关系并说明理由;
(2)猜想验证:莹莹通过测量发现
与
,
与
有同样的数量关系,写出它们的关系并说明理由;
(3)尝试运用:利用(2)的结论计算
的面积;
(4)拓展探究:莹莹把
剪下后得
,发现可以与
拼成四边形,且拼的过程中点
不与点
重合,直接写出拼成四边形时
的长.
教材重现:取一块质地均匀的三角形木板,用一枚铁钉顶在这个三角形的重心上,木板会保持平衡(如图),这是重心的物理性质.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8817091d0f4b7d7ac6df560cb63c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.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/d004d2d115b477ade6af7ddb93db0df8.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)猜想验证:莹莹通过测量发现
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
(3)尝试运用:利用(2)的结论计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbf9680f74a9ac5d934304654ce2771.png)
(4)拓展探究:莹莹把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36691f0269294ecae8f00b7bce97756c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f1c441692afc8ec307b8a563cafef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fce10478485ef01d2318fc3465bb4e.png)
您最近一年使用:0次
2024-06-13更新
|
132次组卷
|
3卷引用: 2024年山东省聊城临清市中考二模数学试题