1 . 平行四边形
中,对角线
相交于点O,E、F分别为线段
的两点,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d0b0b7d07ac1aebab6b6f1e8c6acdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b866a4e7ca37c7b6164302190d4789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2742e11fc7d28fc674537e11d09d042c.png)
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2 . 【问题探究】
综合实践课上,老师给出这样一个问题要求同学们进行小组合作探究:
如图①,在
中,
,点
在边
上,
.探究图中线段
之间的数量关系.
小红同学这一个学习小组探究此问题的方法是:
将
绕点
逆时针旋转
,得到
,连接
(如图②),由图形旋转的性质和等腰直角三角形的性质以及
,可证
,得
.即可得出
之间的数量关系.
(1)请你根据小红同学这一学习小组的探究方法,写出探究结论:
在图②中,
______度,
之间的数量关系是______.
(2)小明同学这一学习小组在上述探究的基础上,又进行了如下问题的探究:
如图③,在正方形
中,点
分别是边
上的动点,连接
交
于
,若
.请你帮小明同学这一学习小组完成如下猜想:
①线段
的数量关系是______;
②线段
的数量关系是______;
请任选一个你的猜想说明理由.
(3)请根据上述探究方法,解决如下问题:如图④,已知点
,点
,点
位于
轴正半轴,
,试求出点
的坐标.
综合实践课上,老师给出这样一个问题要求同学们进行小组合作探究:
如图①,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40975f7553d8cfa57951b568bae9c464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76805974fefbe166b90d260e822ab5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da1ed3760e330be3bad2699caefd238.png)
小红同学这一个学习小组探究此问题的方法是:
将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76805974fefbe166b90d260e822ab5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0d88f9fbd1ec427ed8681d2a6fefc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cad196e55dbd13c45e11a51d700383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da1ed3760e330be3bad2699caefd238.png)
(1)请你根据小红同学这一学习小组的探究方法,写出探究结论:
在图②中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61b1176b90b7393e539414dd1dd94c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da1ed3760e330be3bad2699caefd238.png)
(2)小明同学这一学习小组在上述探究的基础上,又进行了如下问题的探究:
如图③,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20cb2c77ea29b6eabbc477bc3743859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de9f075d2558b7dce0eb91148de84fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192155e6a3aade305b76b1eb7c75e30c.png)
①线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00beaa467a0e087396b2fad5be8d1840.png)
②线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f48011b39a6a54da007ef4e2878dbd.png)
请任选一个你的猜想说明理由.
(3)请根据上述探究方法,解决如下问题:如图④,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf02334810fe35d00fe99d2945fbfbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914e4d5df26f1967d92d62600cfe3656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81e24376a13d648c2ed0dc73bc710e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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名校
3 . 如图,点
、
、
、
在一条直线上,
且
,
.
;
(2)求证:四边形
是平行四边形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd81adb13f5a7550b0f94f770900a613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7f27111303c38eaf43bf547e460a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d9cc37ac19a35e2bf17921443dbb81.png)
(2)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaecff592cf677f45d8c54340a89f2.png)
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2024-04-26更新
|
540次组卷
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5卷引用:2024年湖南省岳阳市岳阳县中考一模数学试题
2024年湖南省岳阳市岳阳县中考一模数学试题(已下线)数学(山东济南卷)-学易金卷:2024年中考考前押题密卷2024年广西壮族自治区钦州市共美学校中考二模数学试题(已下线)专题6.4 平行四边形的判定(分层练习)(基础练)-2023-2024学年八年级数学下册基础知识专项突破讲与练(北师大版)(已下线)作业03 平行四边形(知识梳理+四大题型专练+能力拓展练)-【暑假分层作业】2024年八年级数学暑假培优练(人教版)
4 . 如图,正方形
边长为4,点
分别在边
上,且满足
交于
点,
分别是
的中点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c05542a52e20690a6263588000bf02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b62b997ff70441a93e187bb04b51be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9dd430e3539fe4f745c1e2d5cd29404.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-04-19更新
|
438次组卷
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5卷引用:数学(湖南长沙卷)-【试题猜想】2024年中考考前最后一卷
数学(湖南长沙卷)-【试题猜想】2024年中考考前最后一卷2024年湖南省衡阳市祁东县育贤中学中考模拟数学试题2024年安徽省芜湖市中考二模数学试题(已下线)重难点06 相似三角形模型及其压轴类型(8大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(广东专用)(已下线)重难点05 四边形压轴类型归纳(9大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(广东专用)
5 . 如图,在矩形
中,点E、F是对角线
上两点,
.
是平行四边形;
(2)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/75edb3996fbf4e47c6065d81adf69d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2330c01a4d2b5b20f106e3e48834d5c0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d320f180419175d75eebc618cc458b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f218914337edd06e59e75d90b777e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-04-19更新
|
166次组卷
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3卷引用:2024年湖南省长沙市立信中学中考一模数学试题
名校
6 . 如图,在
和
中,
,
,
,且点
在线段
上,连接
.
;
(2)若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d212c1709b8e72a055cf1b5381ef64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26813466e2ee49a493881a4384fc8748.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/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b739cfff78fadaeee0db677ecc958d2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e76bbd182f32ad35058af2dc93a2621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
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7 . 如图,矩形
中,
,F是
上一点,E为
上一点,且
,连接
,将
绕着点E顺时针旋转
到
的位置,则
的最小值为 __________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f1844834ef0315a704d8e2fba77544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60634341a9603e24b2bbc6960abe3d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
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8 . 如图
,矩形
中,
,
,点
,
分别在边
,
上,且
,连接
,
,并以
,
为边作平行四边形
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/10/bb47e278-5aee-4a48-b4f7-8c92b04079b4.png?resizew=301)
(1)连接
,求
的长度;
(2)求平行四边形
周长的最小值;
(3)当平行四边形
为正方形时
如图
,连接
,分别交
,
于点
、
,求
:
的值.
![](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/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c114237f609956017bc72f4971d5b375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/10/bb47e278-5aee-4a48-b4f7-8c92b04079b4.png?resizew=301)
(1)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
(2)求平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
(3)当平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad217e26bd3580c35998109de14cef73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](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/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55bb0405afa96ebf94c5b03fd52763dd.png)
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9 . 如图,正方形
的边长为4,点E在
上且
,F为对角线
上一动点,则
周长的最小值为________
![](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/adc90c2d45477e166b02359525f40aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80d32bd31d565cd7a5fa4b42dc2e040.png)
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2024-04-07更新
|
269次组卷
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23卷引用:湖南省邵阳市大祥区2018年中考数学考前押题卷
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