综合与实践
问题情境:
在“综合与实践”课上,老师提出如下问题:如图1,
是线段
上的一点,以
和
为直角边分别作等腰直角
和等腰直角
,点
在边
边上,连接
和
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/729d8307-29e4-4e6e-bc21-8b2ea6d9636e.png?resizew=150)
独立思考:
(1)试判断
和
的位置关系,并说明理由.
实践探究:
(2)“聪慧小组”受此问题的启发,将图
中的
绕着点
逆时针旋转角度
,使得点
落在
的外部,得到
,点
的对应点为
,点
的对应点为
,连接
,
,如图
,请判断
与
之间的位置关系,并加以证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/b7081816-6ee7-4fae-b917-e7c1c5e8d6ab.png?resizew=158)
拓展探究:
(3)“善思小组”奇想:如图
,将
绕着点
逆时针旋转角度
时,得到
,连接
,
交
于点
,延长
交
于点
,该小组提出一个问题:若
是线段
的中点,
的面积为
,求
的面积,请你思考此问题,直接写出该问题的结果.
问题情境:
在“综合与实践”课上,老师提出如下问题:如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b40c2b0ab8e1cfe5112d428b4b829f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/729d8307-29e4-4e6e-bc21-8b2ea6d9636e.png?resizew=150)
独立思考:
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
实践探究:
(2)“聪慧小组”受此问题的启发,将图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7199ded47c047792b3147c25467359c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ee6902d209dfd156f4ae98e59c077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d30252720ff0a2b1f105523e9aa3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d30252720ff0a2b1f105523e9aa3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/b7081816-6ee7-4fae-b917-e7c1c5e8d6ab.png?resizew=158)
拓展探究:
(3)“善思小组”奇想:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c96cb3ac8290e09c55d4eb336a8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ee6902d209dfd156f4ae98e59c077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d30252720ff0a2b1f105523e9aa3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d30252720ff0a2b1f105523e9aa3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73afe528350ff17da6fc586fd617495f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71810d999101380a843fd798aa28355c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/32502ab9-1768-4e1e-b103-9a422b1bffd2.png?resizew=157)
更新时间:2024-02-10 19:44:39
|
相似题推荐
解答题-证明题
|
较难
(0.4)
名校
【推荐1】已知
是等边三角形,点D为平面内一点,连接
、
,
,
下方时,连接
,延长
到点E,使
,连接
.
①求证:
;
②如图②,过点A作
于点F,直接写出线段
、
、
间的数量关系;
(2)若
,
,直接写出点A到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcf905f3910d9238a44ef647835b3d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa80cfd38f59e5cbbb30628d03113689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52273305805769a438772342b53c289e.png)
②如图②,过点A作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876bb8ce0ca53475fa091ffd18bdc94a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f0e783b3f0fdbecacc5cb8612ffcef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00948a72b7c367ccda6badc2f7ff22fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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【推荐2】(1)问题发现:如图1,在
和
中,
,
,点
是线段
上一动点,连接
,填空:
①
的值为_____________ ②
的度数为___________
(2)类比探究:如图2,在
和
中,
,
,点
是线段
上一动点,连接
,请判断
的值及
的度数,并说明理由.
(3)结论应用:如图2,在(2)的条件下,若
,
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2598f844644c4245eb226ecca57ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc75953bf5dcfa4af308c34bf9952d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a356ae65ad2cccdd27189efcea2da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f4907f159ff9c4caacf266db591588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685516a27697104e83b311d76efa17aa.png)
(2)类比探究:如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2598f844644c4245eb226ecca57ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc75953bf5dcfa4af308c34bf9952d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17df03e1b7418a84e8f8a3d512b2c1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f4907f159ff9c4caacf266db591588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685516a27697104e83b311d76efa17aa.png)
(3)结论应用:如图2,在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201a535bbbf5bfe454c2a2c534178fd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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【推荐1】【概念认识】如果
,即
,则b叫做a和c的比例中项,或等比中项.若一个三角形一条边长是另两条边长的等比中项,我们把这个三角形叫做等比三角形.
(1)已知
是等比三角形,
,
.请直接写出所有满足条件的
的长;
【数学理解】
(2)如图1,在四边形
中,
,对角线
平分
,
.求证:
是等比三角形;
【问题解决】
(3)如图2,在(2)的条件下,当
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d4c2b2737fc11f96ecd8e2ae6591f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988b7e964e313579ab8869d67d5be007.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/60ef95894ceebaf236170e8832dcf7e3.png)
【数学理解】
(2)如图1,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](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/83ae683c408ef00f0cd19d50fbeb0d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
【问题解决】
(3)如图2,在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78c44f837a63101c19745cc1a79a740.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/709fc8df-6df1-4ae9-8310-94aa752e113b.jpg?resizew=316)
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解题方法
【推荐2】如图①,在矩形ABCD中,点P从AB边的中点E出发,沿着E﹣B﹣C匀速运动,速度为每秒1个单位长度,到达点C后停止运动,点Q是AD上的点,AQ=10,设△PAQ的面积为y,点P运动的时间为t秒,y与t的函数关系如图②所示.
(1)图①中AB= ,BC= ,图②中m= .
(2)点P在运动过程中,将矩形沿PQ所在直线折叠,则t为何值时,折叠后顶点A的对应点A′落在矩形的一边上.
(1)图①中AB= ,BC= ,图②中m= .
(2)点P在运动过程中,将矩形沿PQ所在直线折叠,则t为何值时,折叠后顶点A的对应点A′落在矩形的一边上.
![](https://img.xkw.com/dksih/QBM/2021/7/1/2754855595196416/2768344603926528/STEM/ddec5e35-bb24-46dc-9ba6-71ed181e2e07.png)
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【推荐1】如图,正方形
中,对角线
,
相交于点
,
,过点
作
,连接
交
边于点
,以
为边向上作正方形
,连接
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac4b005d4e0ef0401b78a8ce3969e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7465c3848d832ec772b6c1510d61aa59.png)
;
(2)当
时,求正方形
的边长;
(3)将正方形
绕点
逆时针旋转,旋转后的正方形记为
(点
,
,
的对应点分别记为点
,
,
,设边
与边
的交点为点
,连接
,当
,且
时,直接 写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995c569ac2b958ec2531e0620084ffec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea542c31170157c0e9b9e8b65a95437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d3a6cadabd98c16868467f855d1637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/7d701be5-9406-48ba-a294-f68c11c56e49.png?resizew=418)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac4b005d4e0ef0401b78a8ce3969e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7465c3848d832ec772b6c1510d61aa59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132986c2d7eb546646054da279000450.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faffe3765c15f53305516895aa595a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d3a6cadabd98c16868467f855d1637.png)
(3)将正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d3a6cadabd98c16868467f855d1637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16063c3a614b33e139724aec4ae34e93.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81722445de00f3cfcc3cb97e45b0d8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d955d197e2ecbfe724570663efcf2a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec1093f2bd72971a21411d53d4fabb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa550aa89622e19818425142163daf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaacaea323891412a167aa7891ca571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b29de20122b203ed5d4a834b885a5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
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解答题-问答题
|
较难
(0.4)
【推荐2】四边形
内接于
,
为直径, E 在
的延长线上,且
与
相切.
平分
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/7037624a-0b27-45f4-8e7c-fd414d3fd69a.png?resizew=192)
(1)判断
与
的位置关系,并说明理由;
(2)若
,
,求
的半径
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6344778ed1e75c1a99e2268468081867.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/7037624a-0b27-45f4-8e7c-fd414d3fd69a.png?resizew=192)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7cbfaec1d9dcaaf159b060163436113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be62ac0f5edb1eaebb5f491a7c30f97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
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