综合与实践
综合与实践课上,老师让同学们以“三角板的平移”为主题开展数学活动.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/35d21c87-cb05-4776-821d-bc17f0a1a511.png?resizew=459)
(1)操作判断
操作一:将一副等腰直角三角板两斜边重合,按图1放置;
操作二:将三角板
沿
方向平移(两三角板始终接触)至图2位置.
根据以上操作,填空:
①图1中四边形
的形状是 ;
②图2中
与
的数量关系是 ;四边形
的形状是 .
(2)迁移探究
小航将一副等腰直角三角板换成一副含
角的直角三角板,继续探究,已知三角板
边长为
,过程如下:
将三角板
按(1)中的方式操作,如图3,在平移过程中,四边形
的形状能否是菱形,若不能,请说明理由,若能,请求出
的长.
(3)拓展应用
在(2)的探究过程中:
①当
为等腰三角形时,请直接写出
的长;
②直接写出
的最小值.
综合与实践课上,老师让同学们以“三角板的平移”为主题开展数学活动.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/35d21c87-cb05-4776-821d-bc17f0a1a511.png?resizew=459)
(1)操作判断
操作一:将一副等腰直角三角板两斜边重合,按图1放置;
操作二:将三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
根据以上操作,填空:
①图1中四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
②图2中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ecdb698bd9d00d684430e911e4d99d.png)
(2)迁移探究
小航将一副等腰直角三角板换成一副含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
将三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ecdb698bd9d00d684430e911e4d99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
(3)拓展应用
在(2)的探究过程中:
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e95b09cec34e6dcdccaaddbc517ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
②直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924e18eb3a97269b62d0d3e2a7a5e884.png)
更新时间:2023-04-23 21:17:07
|
相似题推荐
解答题-证明题
|
较难
(0.4)
【推荐1】已知,如图①,四边形
是矩形,对角线
相交于点O,
.
在图①中,根据给出的条件,直接写出一条未知线段的长度或一个角的大小;
(2)【问题探究】
如图②,在矩形
中,点P是对角线
上的一个动点,连接
,过点P作
交
于点E,连接
,在点P运动的过程中试探究
的大小,并写出证明过程;
(3)【拓展延伸】
如图③,在矩形
中,点P是对角线
上的一个动点,连接
,在
的左下方作
,使
,
,在点P从点B向点D的运动过程中,猜想点Q的运动路径并求出它的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd4699c727a6335540e511d0ac9edb7.png)
在图①中,根据给出的条件,直接写出一条未知线段的长度或一个角的大小;
(2)【问题探究】
如图②,在矩形
![](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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a92bf37efe386e969621baf38d1eb1a.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/1a9b4a78c3b85dafdaec2e4e6dc87bd7.png)
(3)【拓展延伸】
如图③,在矩形
![](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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec07fc1e0cf74270d42f53458713af3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114a5ad325caa9a344eb5dd198413859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5fcdc6174333e0d2e6547e59219b07a.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐2】如图,若一次函数
的图象与
轴,
轴分别交于
,
两点,二次函数
的图象过
,
两点,交
轴另一点
的坐标,顶点为点
,对称轴交
于
,
(1)求抛物线的解析式;
(2)如图1,点
是
上方抛物线上一点.过点
作
轴于
,分别交
、
于
、
,作
于
,
于
,若
,求点
的坐标;
(3)如图2,点
是
上方抛物线上一点.过点
作
轴于
,交
于
,连接
、
,若
中的一个内角是
的2倍,求点
的横坐标
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae652daf6059ff386f99bef2210518c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/4c373f804dc6c00e5db92c71ba921d93.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/9bae9b8e-a2ea-45b5-923f-03a49ac1243c.png?resizew=376)
(1)求抛物线的解析式;
(2)如图1,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae95e96ce568efee50145f8d017353df.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b154270249b0ef54ddb26137b2681a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66fae8e33cd86fa8dab72704eaafe1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793ebb9e7b90a76dcf3d4582e49ff8f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae95e96ce568efee50145f8d017353df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0936e532862712045365cb3f63fced9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ee72b8942479ea23b5246d83c1609e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐1】如图,平行四边形
中,
,
,点
是
边上的点,连接
,以
为对称轴作
的轴对称图形
.
正好落在
边上时,判断四边形
的形状并说明理由;
(2)如图1,当点
是线段
的中点且
时,求
的长;
(3)如图3,当点
,
,
三点共线时,恰有
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35df46d413858ccf400647e117dee605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6e17b7a9d3cf87161512785cb65ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cbe52205e9c724bf7e12a2ccbc02bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bd29802a63ea91037ee8b4d64da44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d558d70f4fbe95a799aa9f123c4cd37.png)
(2)如图1,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c032848d5211ffedd24863bdcbddb6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
(3)如图3,当点
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f083630020e71ab026317fd34ae8b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
名校
【推荐2】如图,一次函数y=kx+b分别交x轴正半轴、y轴正半轴于点A、B,点P在边OA上运动(点P不与点O,A重合),PE⊥AB于点E,点F,P关于直线OE对称,PE:EA=3:4.若EF∥OA,且四边形OPEF的周长为6.
![](https://img.xkw.com/dksih/QBM/2019/12/22/2360410364182528/2360818751504384/STEM/e98b15860cf5440bb762cdf0997e1a40.png?resizew=201)
(1)求证:四边形OPEF为菱形;
(2)求证:OB=BE;
(3)求一次函数y=kx+b的表达式.
![](https://img.xkw.com/dksih/QBM/2019/12/22/2360410364182528/2360818751504384/STEM/e98b15860cf5440bb762cdf0997e1a40.png?resizew=201)
(1)求证:四边形OPEF为菱形;
(2)求证:OB=BE;
(3)求一次函数y=kx+b的表达式.
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
【推荐1】已知
,点
是
的角平分线
上的任意一点,现有一个直角
绕点
旋转,两直角边
,
分别与直线
,
相交于点
,点
.
![](https://img.xkw.com/dksih/QBM/2019/5/20/2207794527862784/2207847216005120/STEM/c4c63a6a8ddf405b8c605d1c83c32593.png?resizew=164)
(1)如图1,若
,猜想线段
,
,
之间的数量关系,并说明理由.
(2)如图2,若点
在射线
上,且
与
不垂直,则(1)中的数量关系是否仍成立?如成立,请说明理由;如不成立,请写出线段
,
,
之间的数量关系,并加以证明.
(3)如图3,若点
在射线
的反向延长线上,且
,
,请直接写出线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f8eff113ca3f0d0200253c7c2f5a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2019/5/20/2207794527862784/2207847216005120/STEM/c4c63a6a8ddf405b8c605d1c83c32593.png?resizew=164)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affbe2d2ced2303d8c3d183746d0bcf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
(2)如图2,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
(3)如图3,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bd1ffa355edcdc023b5a6b47ca7526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804a784b65650412e60099413eed1c2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
【推荐2】探究问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/a8c38b18-3bbe-48b3-bf37-dc3db8c31ecd.png?resizew=456)
(1)如图1,PM、PN、EF分别切
于点A、B、C,猜想
的周长与切线长PA的数量关系,并证明你的结论.
(2)如果图1的条件不变,且
,
的周长为16cm,求
的半径.
(3)如图2,点E是
的边PM上的点,
于点F,
与边EF及射线PM、射线PN都相切.若
,
,求
的半径.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/a8c38b18-3bbe-48b3-bf37-dc3db8c31ecd.png?resizew=456)
(1)如图1,PM、PN、EF分别切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9925407467278420029b8ab7b9561a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7a8631373642cd38b08fd3cdb7b5b4.png)
(2)如果图1的条件不变,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b26a0c6b7794b0145f5c6916f5026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7a8631373642cd38b08fd3cdb7b5b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9925407467278420029b8ab7b9561a.png)
(3)如图2,点E是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007bc9cf425a0255f69b8526dbb7e79e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd59e60915beb3560b24a8952eff04e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9925407467278420029b8ab7b9561a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224d65fe97b54e1aefdcd6fd4aeb2188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a8cab15ebb415e9101f9363a69e52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9925407467278420029b8ab7b9561a.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
【推荐1】如图,
是四边形
的对角线,边
在其所在的直线上平移,将通过平移得到的线段记为
,连接
、
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/88b76c32-5f7e-41aa-bf40-6ee9c21587d9.png?resizew=473)
(1)如图1,四边形
是正方形时,作
,垂足为O,连接
、
.判断
、
之间的数量关系和位置关系,并证明;
(2)如图2,四边形
是菱形时,设
,点O在
上,且
.判断
与
的数量关系,写出推理过程,并用含有
的代数式表示
;
(3)在(2)的条件下,若
,
,当四边形
是菱形时(如图3),请直接写出线段
平移的距离为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c118858379800688c993a8b61270b356.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/88b76c32-5f7e-41aa-bf40-6ee9c21587d9.png?resizew=473)
(1)如图1,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b9fd7a5b10127e9d60f0e3fa335f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
(2)如图2,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597ce705d3a2fe04d29de9e81ec6250d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7ce7266232225de08d7c92642071c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3a3bf63440a2fdd769162516fb0e1c.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6850a299395c314b8f8f2f8ca50c9895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1337ce85d29edabcc2fadb9a9cc31ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bddc68ed03fe7fd1fe30a5e626ba435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐2】已知点
,点
,点
,且
.
(1)求
,
,
三点的坐标:
(2)将线段
平移到线段
,点
对应点
,点
对应点
.
交
轴于点
,求三角形
的面积;
②如图2,点
从原点
出发以
个单位长度
秒的速度沿
轴正方向运动,过点
作
的平行线交
轴于点
,点
在直线
上,设点
运动时间为
秒,当三角形
的面积等于三角形
面积的两倍时,直接写出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40aaa43c219bd035f09cc00cf3e15071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95828f5f4aa9100a71cb53c9b113447.png)
(1)求
![](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)将线段
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f8aec2fde514a1c6b7627c024af9d6.png)
②如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e867e5eac6de1647a9ede91ffa083f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d16c639cfa273a0b0f99bd9c725a10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
解答题-作图题
|
较难
(0.4)
名校
【推荐3】综合与实践
探索图形平移中的数学问题
问题情境:如图
,已知
是等边三角形,
,点
是
边的中点,以
为边,在
外部作等边三角形
.
操作探究:将
从图
的位置开始,沿射线
方向平移,点
,
,
的对应点分别为点
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/ab5739f1-df6b-4a5b-adcc-17afb2555d12.png?resizew=442)
(1)如图
,善思小组的同学画出了
时的情形,求此时
平移的距离;
(2)如图
,点
是
的中点,在
平移过程中,连接
交射线
于点
,敏学小组的同学发现
始终成立
请你证明这一结论;
拓展延伸:(3)请从
,
两题中任选一题作答,我选择______ 题
A.在
平移的过程中,直接写出以
,
,
为顶点的三角形成为直角三角形时,
平移的距离.
B.在
平移的过程中,直接写出以
,
,
为顶点的三角形成为直角三角形时,
平移的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b647ade22a4b2a37f8d14141b773744.png)
问题情境:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
操作探究:将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/ab5739f1-df6b-4a5b-adcc-17afb2555d12.png?resizew=442)
(1)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b688d1952e060fc33ce8dc258723bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
(2)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e07b15cfb3b56c8a836832a85c0d1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbdf5716213bd6ddc5b0da5dd0d1487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d044f81c35898999912354c7e17e0c.png)
拓展延伸:(3)请从
![](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/c90282d4a37c9a20620d4bbb0c263cae.png)
A.在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
B.在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
您最近一年使用:0次