1 . 某数学兴趣小组在数学课外活动中,对多边形内两条互相垂直的线段做了如下探究:
(
)如图
,在正方形
中,点
分别是
上的两点,连接
,
,则
的值为__________.
(
)如图
,在矩形
中,
,
,点
是
上的一点,连接
,且
,则
的值为__________;
【类比探究】
(
)如图
,在四边形
中,
,点
为
上一点,连接
,过点
作
的垂线交
的延长线于点
,交
的延长线于点
,求证:
.
【拓展延伸】
(
)如图
,在
中,
,
,
,将
沿
翻折,点
落在点
处得
,点
分别在边
上,连接
,
,
.求
的值.
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137717f0e360e82319ced7e3a6c69b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21cc3c5593dee883a54618c948ca8807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a128183b4d191a765ef19ff41aecc43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ada5e380d6b5b2066e34497e5f0baf0.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c1e75eb744576c32eed3f9d20f9558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.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/c0fe1363ef62726e068550cf6b145596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45b04cc3e5adaeff6f9e01e29032803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8775dcf60ad143bc59a58b000f374c56.png)
【类比探究】
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41aba1711910c6f533cc94319104f4fd.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/ccb545c1a90c841d0d25070cf62b64e3.png)
【拓展延伸】
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16834582e86f9c1030a4a4b316fab909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a306417e43670260e4b68a928a22071f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53289e3083b05d556dd30197abc547ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/73636989e83905f8800a865c2b608c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137717f0e360e82319ced7e3a6c69b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f87b02b744534ae1ed700d21fcceb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ada5e380d6b5b2066e34497e5f0baf0.png)
您最近一年使用:0次
2024-05-12更新
|
322次组卷
|
3卷引用:2023学年贵州省铜仁市碧江区铜仁学院附属中学九年级下学期第5次模拟预测题
2023学年贵州省铜仁市碧江区铜仁学院附属中学九年级下学期第5次模拟预测题2024年广东省阳江市阳春市中考一模数学试题(已下线)考前特训03 几何解答题探究综合压轴题-2024年中考数学二轮热点题型归纳与变式演练(全国通用)
2 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.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/9d78abbad68bbbf12af10cd40ef4c353.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa1aa5a7a5bb172ed4603f17c8b2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf7e12dc03db7186feae41fd1751499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd1f3b67f266fc83774bc59ef8b90a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)【问题探究】如图②,直角三角形纸片
![](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/8455657dde27aabe6adb7b188e031c11.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/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f913298f0fae9f55377a8deab9f099dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(3)【拓展延伸】如图③,在等腰直角三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/3efffb3e6a571832b723b3c5795b8e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2024-04-26更新
|
89次组卷
|
4卷引用:2023年贵州省贵阳市修文县初中学业水平考试数学模拟预测题
3 . 已知点O是线段的中点,点P是直线l上的任意一点,分别过点A和点B作直线l的垂线,垂足分别为点C和点D.
(1)【问题呈现】
如图1,当点P与点O重合时,请你猜想,验证后直接写出和
的数量关系是_______;
(2)【类比探究】
如图2,当点P是线段上的任意一点时,
和
的数量关系是否依然成立?若成立,请给出证明;若不成立,请说明理由;
(3)【拓展提升】
如图3,①当点P是线段延长线上的任意一点时,
和
的数量关系是否依然成立?若成立,请给出证明;若不成立,请说明理由;
②若,请直接写出线段
之间的数量关系.
您最近一年使用:0次
名校
解题方法
4 . (1)问题探究;如图1,在正方形
中,点E,Q分别在边
上,
于点O,点G,F分别在边
上,
.
①判断
与
的数量关系:
______
;②推断:
的值为________;
(2)类比探究,如图(2),在矩形
中,
(k为常数),将矩形
沿
折叠,使点A落在
边上的点E处,得到四边形
交
于点H,连接
交
于点O.试探究
与
之间的数量关系,并说明理由;
(3)拓展应用.如图3,四边形ABCD中,
,点M、N分别在边
上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdba2ac1a72eea482f5578843e00357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8681dc7b0483bb527802389b03129b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b37e6adf86f4e108cd5bae7d9d4941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bbdea60708bebc259452cc5e07ea5a.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f12d3876f1b0ffaf9179fb85c0e683.png)
(2)类比探究,如图(2),在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714c979d980d5377a6cc93a452bffe8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872beec7fc07d9aebfb3b928104813f6.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/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/2c778b43-4021-4207-85ae-f592b92a9834.png?resizew=141)
(3)拓展应用.如图3,四边形ABCD中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02626782dc3d343b26daf85532d6c4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdba2ac1a72eea482f5578843e00357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f710f8f1fa0df203765d18692ded6a91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/c1d14dad-681a-48e1-a7ed-61a7bd1f6d2d.png?resizew=170)
您最近一年使用:0次
2023-10-08更新
|
367次组卷
|
6卷引用:四川省成都市武侯区四川大学附属中学西区学校2023-2024学年九年级上学期期中数学试题
名校
5 . (1)【探究发现】如图①,已知矩形
的对角线
的垂直平分线与边
,
分别交于点E,F.求证:四边形
是菱形;
分别交矩形
的边
,
于点E,F,将矩形
沿
翻折,使点C的对称点与点A重合,点D的对称点为
,若
,
,求四边形
的周长;
(3)【拓展延伸】如图③,直线
分别交平行四边形
的边
,
于点E,F,将平行四边形
沿
翻折,使点C的对称点与点A重合,点D的对称点为
,若
,
,
,求
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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9766e5eb6796dafc5ffe212afdfc43c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
(3)【拓展延伸】如图③,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b173ac8cc4ac4f1c9e1daaa605fbb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2024-04-05更新
|
678次组卷
|
22卷引用:江苏省南通市海安市西片联盟2022-2023学年八年级下学期期中数学试题
江苏省南通市海安市西片联盟2022-2023学年八年级下学期期中数学试题2023年山东省青岛第二十六中学中考二模数学试题(已下线)八年级下学期数学期末质量检测B卷(测试范围:八下全部内容)-【单元测试】2022-2023学年八年级数学下册分层训练AB卷(人教版)湖北省利川市五校教联体2022-2023学年八年级下学期期中数学试题湖北省黄石市四区2022--2023学年八年级下学期期末数学试题(已下线)2023年青岛二模(探究拓展题)湖北省武汉市湖北大学附属中学2023-2024 学年九年级上学期月考数学试题湖北建始县官店镇民族中学2023-2024学年九年级上学期月考数学试题广东省佛山市三水区西南中学2023-2024学年九年级上学期第一次月考数学试题2023年四川省绵阳市涪城区中考模拟预测九年级数学模拟预测题2023年四川省绵阳市涪城区中考数学终极模拟预测题(6月份)湖北省襄阳市枣阳市2021-2022学年八年级下学期期末数学试题甘肃省武威市武威第十中学2023-2024学年九年级下学期第一次月考数学试题(已下线)专题17八年级期中压轴题精选-【好题汇编】备战2023-2024学年八年级数学下学期期中真题分类汇编(人教版,湖北专用)江西省南昌市一中教育集团2023-2024学年八年级下学期期中数学试题(已下线)名校期中好题汇编(人教版八年级数学下册):专题四——特殊平行四边形(已下线)考前特训03 几何解答题探究综合压轴题-2024年中考数学二轮热点题型归纳与变式演练(全国通用)江苏省南通市如东县2023-2024学年八年级下学期期中数学试题广东省江门市福泉奥林匹克学校2023-2024学年八年级下学期期中数学试题(已下线)专题06四边形折叠问题与最值问题(优选33道)-【好题汇编】备战2023-2024学年八年级数学下学期期末真题分类汇编(湖北专用)(已下线)专题05特殊的平行四边形(六大题型优选50道)-【好题汇编】备战2023-2024学年八年级数学下学期期末真题分类汇编(湖北专用)(已下线)2023—2024学年名校期末好题汇编(人教版八年级数学下册)——专题四—特殊的平行四边形
6 . 如图1,两个全等的直角三角形
和
的斜边
和
在同一直线上,
,将
沿直线
平移,并连接
,
.
【基础巩固】
(1)求证:在
沿直线
平移过程中,四边形
是平行四边形;
【操作思考】
(2)如图2,已知
,当
沿
平移到某一个位置时,四边形
为菱形,求此时
的长;
【拓展探究】
(3)如图3,连接
,若四边形
为菱形,且
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
【基础巩固】
(1)求证:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
【操作思考】
(2)如图2,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ded3fed7f7c6d4183b12ad97f5d625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
【拓展探究】
(3)如图3,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024dc2ccbbe321774df5d44e8785b203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
您最近一年使用:0次
7 . (1)【证明推断】如图,在正方形
中,点E是对角线
上的动点(与点B、D不重合),连接
,过点E作
,
,分别交直线
于点F、G.
;
② 求
的值;
(2)【类比探究】如图,将(1)中的“正方形
”改为“矩形
”,其他条件均不变.
,
,求
的值;
② 若
,直接写出
的值(用含m的代数式表示);
(3)【拓展运用】如图,在矩形
中,点E是对角线
上一点(与点B、D不重合),连接
,过点E作
,
,分别交直线
于点F、G,连接
,当
,
,
时,求
的长.
![](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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a19339adac3a2f1aab1fbc11b1c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52cd81afc27aa4b51f3d41c953e22964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240dfffb3b4f1cd83ad8f9a1b8ac9b5a.png)
② 求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd01a4cbd347fce1a7414eb9fa73d16.png)
(2)【类比探究】如图,将(1)中的“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/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd01a4cbd347fce1a7414eb9fa73d16.png)
② 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8035f56ec80c9351e45e964c603d526f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd01a4cbd347fce1a7414eb9fa73d16.png)
(3)【拓展运用】如图,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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a19339adac3a2f1aab1fbc11b1c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52cd81afc27aa4b51f3d41c953e22964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1d267eeb09c171c3e847f0597be31c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
8 . 已知在矩形
中,
,
是边
,
上的点,过点
作
的垂线交边
于点
.
[发现]如图1,以
为直径作
,点
(填“在”或“不在”
上;当
时,
的值是 ;
[论证]如图1,当
时,求证:
;
,
是边
,
的中点时,若
,
,求
的长;
[拓展]如图3,将矩形换为平行四边形,在平行四边形
中,
,
,
,
是边
上的动点,过点
在
的右侧作
的垂线
,且有
,当点
落在平行四边形
的边所在的直线上时,直接写出
的长.
![](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/a0ed1ec316bc54c37c4286c208f55667.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
[发现]如图1,以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eea50af37ec3c5239b6380ba93a8c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/690b9df22eece983a7bb54dcacd7aad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d444f27f1ea9d7781d52749162e304c.png)
[论证]如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd93954f2eb03f0975dc7fab6a228ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d974e36af6dd9fe844201c3ebeecebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df77cc6f8b81245d2699132b6d9f3ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
[拓展]如图3,将矩形换为平行四边形,在平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cbab64c34b6317ee4c68ba7f8d56c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d1f14871d90e2bf98a8cf740515ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daf6086ccfe0d8ad065cec6a1ac7fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
您最近一年使用:0次
9 . 综合与实践
问题情境:
如图1,
中,
,
,点C在直线l上,点A、B在直线l的同侧,过点A作
于点D.
(1)如图1,在直线l上取点E,使
.则
与
的数量关系是__________,此时
、
、
之间的数量关系是___________.
探究证明:
(2)如图2,在直线l上取点F,使
,猜想
与
的数量关系,并说明理由(辅助线提示:过点B作
于点H)
拓展延伸:
(3)在直线l任取一点P,连接
,以点P为直角顶点作等腰直角三角形
,作
于点N,请分别探索在图3,图4中
、
、
之间的数量关系,直接写出答案.
问题情境:
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13b505788d3d02bf232ac637fc3a8ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/18/bbec71a3-e9dd-4da0-bf53-9299cca702b4.png?resizew=343)
(1)如图1,在直线l上取点E,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e72d26eae9a5470ac982541c609b109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
探究证明:
(2)如图2,在直线l上取点F,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680b53673467d5e29454148104e32fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425da1ac2faaf900decf12b9f3806340.png)
拓展延伸:
(3)在直线l任取一点P,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fa97340e8bf29c8d81dd77e13a6f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33a3f384acb53b5a21521a77ac0b1f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/18/0b8163b1-f132-4154-ac03-2f9d7ae72f20.png?resizew=429)
您最近一年使用:0次
23-24八年级上·浙江·期末
10 . 【观察发现】
如图,将含有
的三角板的直角顶点放在直线l上,过两个锐角顶点分别向直线l作雨线,这样就得到了两个全等的直角三角形.这种三个直角的顶点都在同一条直线上的基础图形在数学解题中被广泛使用.
【探究迁移】
(1)如图1,在平面直角坐标系中,直线
与x轴,y轴分别交于A,B两点.
①则
;
②C,D是正比例函数
图象上的两个动点,连接
,若
,则
的最小值是 ;
(2)如图2,一次函数
的图象与y轴,x轴分别交于A,B两点.将直线
绕点A逆时针旋转
得到直线l,求直线l对应的函数表达式;
【拓展应用】
(3)如图3,点A在x轴负半轴上,
,过点A作
轴交直线
于点B,P是直线
上的动点,Q是y轴上的动点,若
是以动点Q为直角顶点的等腰直角三角形,请直接写出所有符合条件的点Q的坐标.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/99445a40-a6da-4d46-9db3-802092b811c1.png?resizew=181)
如图,将含有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
【探究迁移】
(1)如图1,在平面直角坐标系中,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c48c439ef919695d2660d0a63e6eb2.png)
①则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a00d6c5d80f95848a61f305e6bc394.png)
②C,D是正比例函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11944f055fd806016ae3576019d4bf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9e085f74723387d61b262c92903e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)如图2,一次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f857fd62125bc25e7aa3a7cbc6f89de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
【拓展应用】
(3)如图3,点A在x轴负半轴上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ea2ed91a9d38a44ff9422648dfed4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24624dffd30b66a5e4de57362b32b2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326218f8cb74103ef06fa26a790f9a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326218f8cb74103ef06fa26a790f9a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/99445a40-a6da-4d46-9db3-802092b811c1.png?resizew=181)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/81e2e80d-3b8a-45e1-b550-a68c41a72fa3.png?resizew=456)
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