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)
2024·广东汕头·一模 查看更多[1]
(已下线)2024年广东省汕头市龙湖区翠英中学中考一模数学试题
更新时间:2024-04-26 11:13:14
|
相似题推荐
解答题-证明题
|
困难
(0.15)
解题方法
【推荐1】将正方形ABCD放置在平面直角坐标系中,B与原点重合,点A的坐标为
,点E的坐标为
,并且实数a,b使式子
成立.
(2)
,且EF交正方形外角的平分线CF于点F.
①如图①,求证
;
②如图②,连接AF交DC于点G,作
交AE于点M,作
交AF于点N,连接MN,求四边形MNGE的面积.
(3)如图③,连接正方形ABCD的对角线AC,若点P在AC上,点Q在CD上,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ddc2bf1c603c963dc50aa4575913b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d4f120b4be85cd566a1386f830a65d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57bfba0696cc7d07363bb77cfdbc257.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7521601ac1fbc4a52d4fe44be9c8e88c.png)
①如图①,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3767efa8adfb71001ad39df9560cbf6a.png)
②如图②,连接AF交DC于点G,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d4259eb51ab725509fd1647fc9b2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec7e18f75afead8bc2f42a4f1e50254.png)
(3)如图③,连接正方形ABCD的对角线AC,若点P在AC上,点Q在CD上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51dfab0c1ec275ff83d08c7293968c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aa6ae6534e61c61a163efa2b217193.png)
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【推荐2】【模型发现】如图1,在正方形
中,E为边
上一点(不与点B、C重合),过点D作垂直于
的一条直线
,垂足为G,交
于点F.小明发现可以通过证明:
得
(不需证明)
【模型探究】(1)如图2,在正方形
中,P为边
上一点(不与点B、C重合),M为线段
上一点(不与C、D重合),过点M作
,垂足为G,交
于点N,请直接写出
与
及线段
、
、
之间的数量关系.
(2)如图3,在(1)的条件下,若垂足G恰好为
的中点,连接
,交
于点H,连接
并延长交边
于点I,再连接
,请探究线段
、
的数量关系;
【拓展应用】(3)如图4,若正方形
的边长为8,点M、N分别为边
、
上的点,过A作
,已知
,将正方形
沿着
翻折,
的对应边
恰好经过点A,连接
交
于点Q.过点Q作
,垂足为R,求线段
的长.(直接写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d0c8d6f1e2508adbeb0d7325fae578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff56ea00ca90825f3d95809de24f639.png)
【模型探究】(1)如图2,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcabbb4a3204d94675ce39838e13c3af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
(2)如图3,在(1)的条件下,若垂足G恰好为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
【拓展应用】(3)如图4,若正方形
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38368ada9cc42339dcffee1b27518940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87f9586b708869fd7186e75a75c1dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/e737bc35da650eda3825d29799b5f86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83847bf2e9122ea6a025efd87bd535f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25b9118da521b6f61f5534c725b7677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/27/d504b635-937e-46c9-bad9-dbd1d7478060.png?resizew=439)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
名校
解题方法
【推荐1】矩形ABCO中,O(0,0),C(0,3),A(a,0),(a≥3),以A为旋转中心顺时针旋转矩形ABCO得到矩形AFED.
(1)如图1,当点D落在边BC上时,求BD的长(用a的式子表示);
(2)如图2,当a=3时,矩形AFED的对角线AE交矩形ABCO的边BC于点G,连结CE,若△CGE是等腰三角形,求直线BE的解析式;
(3)如图3,矩形ABCO的对称中心为点P,当P,B关于AD对称时,求出a的值,此时在x轴、y轴上是否分别存在M,N使得四边形EFMN为平行四边形,若存在直接写出M,N坐标,不存在说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/cd08f44c-67c1-4c33-9acb-17768f0df74e.png?resizew=456)
(1)如图1,当点D落在边BC上时,求BD的长(用a的式子表示);
(2)如图2,当a=3时,矩形AFED的对角线AE交矩形ABCO的边BC于点G,连结CE,若△CGE是等腰三角形,求直线BE的解析式;
(3)如图3,矩形ABCO的对称中心为点P,当P,B关于AD对称时,求出a的值,此时在x轴、y轴上是否分别存在M,N使得四边形EFMN为平行四边形,若存在直接写出M,N坐标,不存在说明理由.
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名校
【推荐2】如图1,已知正方形
中,
为对角线,边长为3,
为边
上一点,过
点作
于
点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/4405328f-bdd0-4568-add4-9ebe271d1433.png?resizew=432)
(1)如图1,连结
,求线段
的长.
(2)保持
不动,将正方形
绕
点旋转至如图2的位置,连结
,
点为
的中点,连接
、
,探求
与
关系,并证明你的结论;
(3)保持
不动,将正方形
绕
点旋转一周,求出
的中点
在这个过程中的运动路径长及
的最小值.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c672f693a7e75a7bae4936dcb1920430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6469878a955cc09fac22ba5aea3fb962.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/4405328f-bdd0-4568-add4-9ebe271d1433.png?resizew=432)
(1)如图1,连结
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
(2)保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
(3)保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
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解答题-问答题
|
困难
(0.15)
【推荐1】如图,抛物线y=ax2+bx﹣4交x轴于A,B两点,交y轴于点C,OB=2OC=4OA,连接AC,BC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/19/5bf834e5-b219-4388-bdb0-62405e4f9cd2.png?resizew=195)
(1)求抛物线的解析式;
(2)点D是抛物线y=ax2+bx﹣4的图象上在第四象限内的一动点,DE⊥x轴于点E,交BC于点F.设点D的横坐标为m.
①请用含m的代数式表示线段DF的长;
②已知DG∥AC,交BC于点G,请直接写出当
时点D的坐标.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/19/5bf834e5-b219-4388-bdb0-62405e4f9cd2.png?resizew=195)
(1)求抛物线的解析式;
(2)点D是抛物线y=ax2+bx﹣4的图象上在第四象限内的一动点,DE⊥x轴于点E,交BC于点F.设点D的横坐标为m.
①请用含m的代数式表示线段DF的长;
②已知DG∥AC,交BC于点G,请直接写出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2e9396ad4e823a20314300fa346854.png)
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解答题-证明题
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【推荐2】如图,长方形纸片ABCD中,AB=8,将纸片折叠,使顶点B落在边AD上的E点处,折痕的一端G点在边BC上.
(1)如图1,当折痕的另一端F在AB边上且AE=4时,求AF的长;
(2)如图2,当折痕的另一端F在AD边上且BG=10时,
①求证:△EFG是等腰三角形;②求AF的长;
(3)如图3,当折痕的另一端F在AD边上,B点的对应点E到AD的距离是4,且BG=5时,求AF的长.
(1)如图1,当折痕的另一端F在AB边上且AE=4时,求AF的长;
(2)如图2,当折痕的另一端F在AD边上且BG=10时,
①求证:△EFG是等腰三角形;②求AF的长;
(3)如图3,当折痕的另一端F在AD边上,B点的对应点E到AD的距离是4,且BG=5时,求AF的长.
![](https://img.xkw.com/dksih/QBM/2020/3/5/2413008797294592/2413172771749888/STEM/022d7df8c7464b978039fcd1cc48d7a1.png?resizew=488)
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