1 . 如图,在长方体
中,
,
是
上一点,
,设
.
的值;
(2)设
,
,
的截面交
于
.
①求证:
;
②设
,截面
将长方体分成两部分,记含
点部分体积为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebecdc0f0f815ff0083d85d3f539b36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2d21ad475ed2176e3f989fde27b849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd6fa050a6df446e6c1cc187549f8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/537f007215286bb97a3f23b2f1617608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4171e7f713d6b265d56b2662b7af57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd93ad139410a0bc761cce65c84f599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b6c72fee28b9f6a2ca8378ad88aa0f.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6beec7ea20dbfffd77e3d1e2b0bda5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
名校
2 . 如图所示,已知多面体
中,四边形
为菱形,
为正四面体,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/8aed5a62-e5b8-475e-9aed-725f94c3ee4c.png?resizew=192)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fc1129846f37afdafd751627c450d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7045cee264e93b07cdf00012bd881a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/8aed5a62-e5b8-475e-9aed-725f94c3ee4c.png?resizew=192)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22eea13efafb003e7b08a6f0bc0f2f3.png)
您最近一年使用:0次
2020-05-03更新
|
307次组卷
|
4卷引用:湖北省襄阳市襄州区第一高级中学2022-2023学年高二上学期9月月考数学试题
解题方法
3 . 如图,四棱锥
的底面是边长为8的正方形,四条侧棱长均为
,点G.E.F.H分别是棱PB.AB.DC.PC上共面的四点,
平面GEFH.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/aeb07114-052f-4990-b353-2b30b7728204.jpg?resizew=190)
(1)证明:
;
(2)若
,平面
平面GEFH,求四边形GEFH的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20ac4a1ec023ef41014cb7730cf8ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/aeb07114-052f-4990-b353-2b30b7728204.jpg?resizew=190)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29dd8914518df1e2c2899f7fbb00336d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07dd741bc3f02d8552afbcf63fba4fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278f7660c3a4949eed798180f92cf442.png)
您最近一年使用:0次
4 . 如图,
平面
,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/230d040e-5b63-4ded-8f42-2f94ea40a684.png?resizew=190)
(Ⅰ)求证:
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f555fb7ea6e77a6e0fe38586a3992d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88dac2c17c765517c2163ab43bbe1038.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/230d040e-5b63-4ded-8f42-2f94ea40a684.png?resizew=190)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2020-04-13更新
|
703次组卷
|
5卷引用:湖北省新高考联考协作体2022-2023学年高二上学期期末模拟数学试题
湖北省新高考联考协作体2022-2023学年高二上学期期末模拟数学试题湖北省恩施州咸丰春晖学校2022-2023学年高二下学期3月月考数学试题浙江省温丽联盟2019-2020学年高三上学期第一次联考数学试题(已下线)专题18 立体几何综合(解答题)-冲刺2020高考跳出题海之高三数学模拟试题精中选萃(浙江专版)2023-2024学年高二上学期期末数学仿真模拟试题02(新高考地区专用)
5 . 如图,已知平面
平行于三棱锥
的底面
,等边
所在的平面与底面
垂直,且
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5ae7ea0163c2fbafbf0af5de03803d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/7c5418cd-5c38-4c5a-aba8-f42f3436f352.png?resizew=158)
(1)求证:
且
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c48cda31ed4fb23b03721e76bd47347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ba5383e768dc86e1bfd79c10f96f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5ae7ea0163c2fbafbf0af5de03803d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/7c5418cd-5c38-4c5a-aba8-f42f3436f352.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23d95dcf2912f4ecb4c4b68bb8108c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf6bb2667203e9e3444ff94f402f0e0.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07603856df484739f00c4f19905f3ae0.png)
您最近一年使用:0次
名校
6 . 如图,在四棱锥S-ABCD中,底面ABCD是菱形,
,
为等边三角形,G是线段SB上的一点,且SD//平面GAC.
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412900907646976/2416012291588096/STEM/ad120724-3b23-4e3d-806e-96b20e8aa732.png)
(1)求证:G为SB的中点;
(2)若F为SC的中点,连接GA,GC,FA,FG,平面SAB⊥平面ABCD,
,求三棱锥F-AGC的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25df618ec33cee978f79d2eae62024f2.png)
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412900907646976/2416012291588096/STEM/ad120724-3b23-4e3d-806e-96b20e8aa732.png)
(1)求证:G为SB的中点;
(2)若F为SC的中点,连接GA,GC,FA,FG,平面SAB⊥平面ABCD,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
您最近一年使用:0次
2020-03-09更新
|
517次组卷
|
5卷引用:2020届湖北省武汉市高三下学期2月调考仿真模拟数学文科试题
名校
7 . 如图1,矩形
中,
,M是
边上异于端点的动点,
于点N,将矩形
沿
折叠至
处,使面
面
(如图2).点E,F满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/91c9d39e-9f7e-4d41-9157-5376b9d05328.png?resizew=453)
(1)证明:
面
;
(2)设
,当x为何值时,四面体
的体积最大,并求出最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9639896487e6cf18e8fd02d2a7ed2087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab384f2520d76ed8fa01b31e09c1eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80a0e428cb894bfd09a6129a73ea4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a47ca365469c996a6b8cb47284764f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46efd4004cc47ba16d3d53b07d40b145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e825de4e5ade72e45a28c8f75b1dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b04eeb552bee53eda166bfb2b85578.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/91c9d39e-9f7e-4d41-9157-5376b9d05328.png?resizew=453)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e787bb792dcd936cb4e87023c95011b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f780ed359b94450fc80cf57e66a4ad8.png)
您最近一年使用:0次
2019-02-05更新
|
710次组卷
|
2卷引用:【全国百强校】湖北省荆州中学、宜昌一中等“荆、荆、襄、宜四地七校考试联盟”2019届高三上学期期末考试数学(文)试题
名校
8 . 如图,在三棱台ABC﹣A1B1C1中,D,E分别是AB,AC的中点,B1E⊥平面ABC,△AB1C是等边三角形,AB=2A1B1,AC=2BC,∠ACB=90°.
![](https://img.xkw.com/dksih/QBM/2019/1/3/2110811852365824/2111689648562176/STEM/91a9089e0c8a45e083aad6aad30ce27c.png?resizew=183)
(1)证明:B1C∥平面A1DE;
(2)求二面角A﹣BB1﹣C的正弦值.
![](https://img.xkw.com/dksih/QBM/2019/1/3/2110811852365824/2111689648562176/STEM/91a9089e0c8a45e083aad6aad30ce27c.png?resizew=183)
(1)证明:B1C∥平面A1DE;
(2)求二面角A﹣BB1﹣C的正弦值.
您最近一年使用:0次
2018-12-03更新
|
1282次组卷
|
6卷引用:湖北省恩施州2017-2018学年高三第一次教学质量监测考试理科数学
解题方法
9 . 如图,在直三棱柱
中,
,
,
,
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/9508bd8c-5b44-43c5-b3e5-e2e6cbac02ca.png?resizew=180)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若异面直线
与
所成角为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cf3bff56a7f4ab6c0008e90823025d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fa098867b1d6e1aeaebe22871821fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02795ff1af51fb0672800ceb02e7893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5dd68e298b39454c148c7a8d951f9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cce34dd995fd1c54a7629fb16c6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4994f75d9a4056bf04228170e27a2658.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/9508bd8c-5b44-43c5-b3e5-e2e6cbac02ca.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f84d1ed2ff6f93bf229c738c58c15c.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17230625e72d3a9c6d72ff61019ff61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8152cb36f666908ce1a748d9f17709dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec1ac46e3ad9d11e07fddb913c53efa.png)
您最近一年使用:0次
2018-07-11更新
|
859次组卷
|
2卷引用:【全国市级联考】湖北省黄冈市2018年春季高一期末考试文科数学试题
10 . 如图,在四面体
中,
在平面
的射影
为棱
的中点,
为棱
的中点,过直线
作一个平面与平面
平行,且与
交于点
,已知
,
.
![](https://img.xkw.com/dksih/QBM/2018/5/25/1953080669855744/1956549983690752/STEM/5d7e1280019b4277a1b8386c8353ce74.png?resizew=176)
(1)证明:
为线段
的中点
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483678f653daf513747f27f3dd6acf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce31c19b0cc9fb8a4986431f933f99e5.png)
![](https://img.xkw.com/dksih/QBM/2018/5/25/1953080669855744/1956549983690752/STEM/5d7e1280019b4277a1b8386c8353ce74.png?resizew=176)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c395fc4390f3f17d18d58c8bc84490.png)
您最近一年使用:0次