2024·广东汕头·一模
名校
1 . 综合与实践课上,梦班数学学习兴趣小组对图形中两条互相垂直的线段间的数量关系进行探究时,遇到以下问题,请你逐一加以解答:
如图1,在正方形
中,点E,F,G,H分别在边
,
,
,
上,且
,若
,则
的长为 ;
如图2,在矩形
中,
,点E,F,G,H分别在边
,
,
,
上,且
,若
,则
的长为 ;
(2)迁移探究
如图3,在
中,
,
,点D,E分别在边
,
上,且
,试证明:
;
(3)拓展应用
如图4,在矩形
中,
,
,
平分
交
于点E,点F为
上一点,
交
于点H,交矩形
的边于点G.当F为
的三等分点时,请直接写出
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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/de64cbea23ec8a57a4705d9f16297d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7c422a19b68b8b4cd484d22897e3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
如图2,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151f7aef7d0f56e18562f5a4030cf815.png)
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de64cbea23ec8a57a4705d9f16297d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e4ceabf0daf448d295489a489a6868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
(2)迁移探究
如图3,在
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c51c25b65a37b676ae3c3b71c29f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bf9b30a14cdedf26b9526097a300e5.png)
(3)拓展应用
如图4,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ebb33adb2310a6e03918761e68204a.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fac5ca06ed1e682ae9ce8e029dbfef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
您最近一年使用:0次
2 . 类比探究题:
【建立模型】
如图1,等腰直角三角形
中,
,
,直线
经过点C,过A作
于点D,过B作
于点E.求证:
.
【应用模型】
如图2,点A的坐标为
,点B是x轴正半轴上的一动点,以
为直角边作等腰直角
,使
,设点B的横坐标为x,点C的纵坐标为y,请写出y与x的函数关系.
【拓展拔高】
如图3,矩形
中,
,
,点P是
边上的一个动点(点P与点B,C都不重合),现将
沿直线
折叠,使点C落到点F处;过点P作
的角平分线交
于点E.设
,
,求y与x的函数关系:y是否有最大值,若有,求出最大值;若没有,说明理由.
【建立模型】
如图1,等腰直角三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323b786e35c9b762d00f2b2ef74ce1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c388d0a3f0a8d9fb0b9576d00af225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c60ab4cdefda079244161bb911a453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83e4f28c096dffd7df54b1162f5b3ae.png)
【应用模型】
如图2,点A的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0efe3c42f37bcb7d6552fdf6261e50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
【拓展拔高】
如图3,矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c0c4e8cd3f3b7939d3010d76564fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a666403569e607f32af5f762c246dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e83115ca0edf2fedb181bb960f3efde.png)
您最近一年使用:0次
3 . 问题情境】已知等腰三角形
中,点D在底边
上.将线段
绕点D顺时针旋转得到线段
(旋转角小于180°),连接
,
,以
为底边在其上方作等腰三角形
,使
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/17/6dbbf0b9-ffa4-4369-9c2c-d91f9a5bb1f5.png?resizew=707)
【尝试探究】
(1)如图1,当
时,易知
;
如图2,当
时,则
与
的数量关系为______.
(2)如图3,探究
与
的数量关系(用含
的三角函数表示),并说明理由.
【拓展应用】
(3)如图4,当
,且B,E,F三点共线时,若
,
,则
的长为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c3f982d999937891eec4cb22d62e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8540871b584dcd428765174e9f8b7c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b34849fd8bb3d2bb8739e1c59de53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/17/6dbbf0b9-ffa4-4369-9c2c-d91f9a5bb1f5.png?resizew=707)
【尝试探究】
(1)如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e444739e269a94733b2b0598b559313.png)
如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c69a23d106fd34aa17b22e9c9a8de36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
(2)如图3,探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
【拓展应用】
(3)如图4,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c96cb3ac8290e09c55d4eb336a8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391daa6ffb8d8f0c69b0680d1130920e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e319ce030f7fe57a9777c7b8f583cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
您最近一年使用:0次
2024-04-22更新
|
128次组卷
|
2卷引用:2024学年甘肃省平凉市初中毕业与高中阶段招生考试模拟数学模拟预测题(一)
名校
4 . 如图,四边形
是菱形,
,点E是
边上一动点,连接
,在
右侧作菱形
使得菱形
菱形
,连接
交
于点R,连接
.
(1)求证:
;
【深入探究】
(2)若R为
中点,求
的值;
【拓展延伸】
(3)①若
,
是等腰三角形,求
的值;
②若D,F,G三点共线,连接
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/a10eec76d00779458ce81639d71c635d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bbe3fda93f6415602f3f8e09a2a649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10eec76d00779458ce81639d71c635d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfe7a6665d1b083d3925ba3ed32b261.png)
【深入探究】
(2)若R为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535ceeaa1cbe8318b1df5efcbebff584.png)
【拓展延伸】
(3)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40560ea08d6cd8c1d4d9661ee6faaa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9d8d9905187fff191215dd4ea5375f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3bd41676f6b69acac00a292fe134cd.png)
②若D,F,G三点共线,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e217e7bba50852cb12c8c4b4646690.png)
您最近一年使用:0次
5 . 综合与实践
“领航”数学研究小组在数学活动中研究了一个问题,请帮他们解答.
实践探究:
四边形
和四边形
都是正方形.
(1)连接
,如图1,试猜想
与
的数量关系,并说明理由;
(2)在(1)的条件下,连接BG,如图2,若
,
,
,则
__________;
(3)连接
,如图3,则
与
的数量关系为__________;
拓展应用:
(4)如图4,四边形
和四边形
都是平行四边形,
,
,且
,
,连接
,则
与
的数量关系为__________.
“领航”数学研究小组在数学活动中研究了一个问题,请帮他们解答.
实践探究:
四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
(1)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3732bf0e4eb3a92543cc1b691f1b361c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
(2)在(1)的条件下,连接BG,如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7095e61966d5128797bcfea5336e0e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26e32412868f3dcb5cad62c8a836778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db9b176f77acb45cc813e22ba1f940c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b846f6f8a3c721825f2ca488fc7f0d.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110c56132dd3c17d9ea4cd326c97fa96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
拓展应用:
(4)如图4,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036d7f2c98f032c74e67277066a6a041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a664f6c707c01e859e9bcdd26072971a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6834ac70927ae08d7d36a1922403c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110c56132dd3c17d9ea4cd326c97fa96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
您最近一年使用:0次
2024-04-19更新
|
150次组卷
|
2卷引用:2024年黑龙江省齐齐哈尔市中考一模数学试题
6 . 在
中,
于点D,点P为射线
上任一点(点B除外),连接
,将线段
绕点P顺时针方向旋转α,
,得到
,连接
.
,且
时,
与
的数量关系是 ,
与
的位置关系是 .
(2)【猜想证明】如图2,当
,且
时,(1)中的结论是否成立?若成立,请予以证明;若不成立,请说明理由.(请选择图2,图3中的一种情况予以证明或说理)
(3)【拓展探究】在(2)的条件下,若
,
,请直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbc28ba86213e215af01cb50e95aaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e4a2df58a236c20df5df0d29a466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)【猜想证明】如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e4a2df58a236c20df5df0d29a466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
(3)【拓展探究】在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574dc284fb9e74d65cf0c79a978d65de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
您最近一年使用:0次
7 . 下面是李老师在“矩形折叠中的相似三角形”主题下设计的问题,请你解答.
如图,已知在矩形中,
,点E为边
上一点(不与点A、点B重合),先将矩形
沿
折叠,使点B落在点F处,
交
于点H.
(1)观察发现
写出图1中一个与相似的三角形: .
(2)迁移探究
当与
的交点H恰好是
的中点时,如图2.
①设,请判断
的数量关系,并说明理由;
②求阴影部分的面积.
(3)拓展应用
当点B的对应点F落在矩形的对称轴上时,直接写出
的长.
您最近一年使用:0次
2023-11-02更新
|
165次组卷
|
2卷引用:广东省深圳市龙岗区百合外国语学校2023-2024学年九年级上学期期中数学试题
8 . 琅琊中学九年级一班同学利用工具,对几种四边形进行探究.
中,该工具与正方形四条边的交点分别为E、F、G、H.
(1)若点O在边长为1的正方形
的中心,直接写出
的最大值和最小值.
(2)试猜想
的值,并证明你的猜想.
【知识迁移】如图2,同学们又将该工具放入矩形
中,该工具与矩形四条边的交点分别为E、F、G、H.若
,
,则
.(直接写出答案)
【拓展运用】如图3,同学们将工具放入四边形
中,使其经过C、B两点,并与
边交于点
,与
边交于点
.已知
,
,
.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)若点O在边长为1的正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219c318e9e61fa301cad75655d433a2b.png)
(2)试猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885a273360456694a3d40a913f3df2fc.png)
【知识迁移】如图2,同学们又将该工具放入矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa375c3888b332f24e7d0f9b9600c694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890aea25780f7ba34adb23e799808462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d852b8a7e7b287c0bae2ce10d3e6dc1.png)
【拓展运用】如图3,同学们将工具放入四边形
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea624cb140001a7e9d7567903a29521.png)
您最近一年使用:0次
9 . 李老师善于通过合适的主题整合教学内容,帮助同学们用整体的、联系的、发展的眼光看问题,形成科学的思维习惯.下面是李老师在“图形的变化”主题下设计的问题,请你解答.
如图1,正方形
中,点
为
边上一点,连接
,过点
作
交
边于点
,将
沿直线
折叠后,点A落在点
处,当
时,
;
如图2,连接
,当点
恰好落在
上时,其他条件不变,则
;
(2)探究迁移
如图3,在(1)的条件下,若把正方形
改成矩形
,且
,其他条件不变,请写出
与
之间的数量关系式(用含
的式子表示),并说明理由;
(3)拓展应用
如图4,在(1)的条件下,若把正方形
改成菱形
,且
,
,其他条件不变,当
时,请直接写出
的长.
如图1,正方形
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f0805cc7a96c866df10b667ac4851e.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/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b13fff157b3ff2b7d80c0cfb3e7a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f331b8b4f9fc690b2e4785c8dd0527dc.png)
如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af9650e51fef805788fe4fea3cfb527.png)
(2)探究迁移
如图3,在(1)的条件下,若把正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52a55bd36f9d239416d7c8fa5d78bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71fe246270d1277f9eb2bf15af22e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)拓展应用
如图4,在(1)的条件下,若把正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284e282bb1d9fbf8634b3506ee5358ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f39dacbcf8ca8364b47ac277beec70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c628297022d4dee189225c9441877539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71fe246270d1277f9eb2bf15af22e83.png)
您最近一年使用:0次
10 . 【探究证明】
(1)某班数学课题学习小组对矩形内两条互相垂直的线段与矩形两邻边的数量关系进行探究,提出下列问题,请你给出证明:
如图①,在矩形
中,
,
分别交
于点E、F,
分别交
于点G、H,求证:
;
【结论应用】
(2)如图②,将矩形
沿
折叠,使得点B和点D重合,若
,求折痕
的长;
【拓展运用】
(3)如图③,将矩形
沿
折叠.使得点D落在
边上的点G处,点C落在点P处,得到四边形
,若
,求
的长.
(1)某班数学课题学习小组对矩形内两条互相垂直的线段与矩形两邻边的数量关系进行探究,提出下列问题,请你给出证明:
如图①,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de64cbea23ec8a57a4705d9f16297d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba48366317ebea1c9dd5e4e67e03092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f0dc39b4e4d3dcbf0baebc83221238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450d0c8cdc114d1d6ba7f69382d9df3e.png)
【结论应用】
(2)如图②,将矩形
![](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/d0eb9ed77d586a7976de01e7551cdb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
【拓展运用】
(3)如图③,将矩形
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0363419eabe432409a7f04598450a396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c414fba9b21b6e8a8035bd6293e7fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/d8fd358a-6156-4334-936c-1d7333e1b22d.png?resizew=164)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/2bf61200-0eef-4840-a16b-e3928558fe1d.png?resizew=150)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/c244c5c8-91d8-494e-8f34-26b238218137.png?resizew=155)
您最近一年使用:0次
2023-10-31更新
|
148次组卷
|
3卷引用:江苏省扬州市梅岭中学教育集团2023-2024学年九年级上学期10月月考数学试题