名校
解题方法
1 . 如图,在长方体
中,
,
,
为
的中点,过
的平面
分别与棱
,
交于点E,F,且
,则截面四边形
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352d5bb010209b795946f7095418115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d918361b03a48660dbd5987cd7a7a3.png)
您最近一年使用:0次
2023-10-27更新
|
552次组卷
|
2卷引用:上海市松江二中2023-2024学年高二上学期10月月考数学试题
名校
解题方法
2 . 如图,正方体
的棱长为2,点
是线段
的中点,过点
做平面
,使得平面
平面
,则平面
与正方形
的交线的长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414844edd458857bdfc80bffa61cbf9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
您最近一年使用:0次
2023-10-24更新
|
613次组卷
|
5卷引用:四川省南充市仪陇县仪陇中学校2023-2024学年高二上学期10月月考数学试题
四川省南充市仪陇县仪陇中学校2023-2024学年高二上学期10月月考数学试题8.5.3平面与平面平行练习(已下线)第10讲 8.5.3 平面与平面平行-【帮课堂】(人教A版2019必修第二册)(已下线)专题19 平面与平面平行-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)11.3.3 平面与平面平行-【帮课堂】(人教B版2019必修第四册)
名校
解题方法
3 . 过平面外一点,可以作这个平面的平行线的条数是( )
A.1条 | B.2条 | C.超过2条但有限 | D.无数条 |
您最近一年使用:0次
名校
解题方法
4 . 如图,在四棱锥
中,
平面
,
,
,
,
分别为
的中点.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487530f6d17b94493d03b004aa3462d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ff6d7dd48b57f03d82d2c522ee9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff65bccc6d801ce84f3f696afee89fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
您最近一年使用:0次
2024-03-16更新
|
884次组卷
|
7卷引用:安徽省安庆市怀宁县高河中学2023-2024学年高二上学期第二次月考数学试题
安徽省安庆市怀宁县高河中学2023-2024学年高二上学期第二次月考数学试题内蒙古呼和浩特市2022届高三第一次质量数据监测文科数学试题(已下线)回归教材重难点03 立体几何-【查漏补缺】2022年高考数学(文)三轮冲刺过关广西南宁市第三中学2021-2022学年高一下学期期中考试数学试题江西省宜春市丰城拖船中学2023-2024学年高二上学期期中数学试题(已下线)黄金卷02(已下线)重难点专题15 空间中的五种距离问题-【帮课堂】(苏教版2019必修第二册)
名校
5 . 如图,
是三棱锥
的高,
,
,E是
的中点.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
平面
;
(2)若
,
,
.
①求二面角
所成平面角的正弦值;
②在线段
上是否存在一点M,使得直线
与平面
所成角为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/69e8805a-ae67-4882-8081-b0a2cb4f11e6.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efea2119d6394d8b34e7b58e5306ce06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764829cc2c763b6aca0665aa143e304e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3015db5ca1f49bb7bad43657e06863ed.png)
①求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53eab3d46050258e079f1bcfced25c0e.png)
②在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
您最近一年使用:0次
6 . 在棱长为4的正方体
中,
分别为线段
上的动点,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9369aed2d8309af46ac3eaffb9cce537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0e216458bc51c77e0934b57e43e96c.png)
A.![]() ![]() |
B.过![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.当三棱锥![]() ![]() |
您最近一年使用:0次
解题方法
7 . 如图,正方形
与梯形
所在平面互相垂直,已知
,
,
.
(1)求证:
平面
.
(2)线段
上是否存在点M,使平面
平面
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5408641691fd27f6dd8cf0ab2043ad4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ae5f8381ffcce4281a0ca817b82a41.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/21/93667f7c-593c-418d-b3c2-16a4c960decb.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f2eae3483395cc6aca5160c64f83eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7084fef1f20c7af36659c1faa643ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cada49bc5cf1cf8615eaf91863d18535.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥
中,底面
是矩形,其中
,
,
底面
,
,
为
的中点,
为
的中点.
(1)证明:直线
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/68e9d843-fc85-4db1-837e-3af70dd6a431.png?resizew=144)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
您最近一年使用:0次
2023-10-18更新
|
822次组卷
|
2卷引用:上海市进才中学2024届高三上学期10月月考数学试题
名校
解题方法
9 . 如图,在四面体
中,
是
中点,
是
中点.在线段
上存在一点
,使得
平面
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412b394ab196e93ba49f115d0a8cacd6.png)
A.1 | B.2 | C.3 | D.![]() |
您最近一年使用:0次
名校
10 . 如图,在三棱柱
中,
平面
,点
,
分别在棱
和棱
上,且
为棱
中点.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91f0d1a4e368147e3783c9374461b3c.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8379e02133be85a72747674b14f86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/bcd417f3-2372-40f6-9065-4f82b3115e7e.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0278f9809e118b80c9946d9b9ae40c83.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd657e48b15b9b54a55817e2c26b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024d58baa25d2565912a9e6e3a06dbe2.png)
您最近一年使用:0次
2023-10-18更新
|
627次组卷
|
2卷引用:辽宁省六校协作体2023-2024学年高二上学期10月联考数学试题