1 . 如图,已知平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
平面
,
与
分别是棱长为1与2的正三角形,
//
,四边形
为直角梯形,
//
,
,点
为
的重心,
为
中点,
.
![](https://img.xkw.com/dksih/QBM/2016/11/22/1573167655288832/1573167661498368/STEM/0cf6f921b91a40898df3ad2dc873ba7f.png?resizew=222)
(Ⅰ)当
时,求证:
//平面
;
(Ⅱ)若直线
与
所成角为
,试求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634979dfcebf857b20874dd320d80b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f1caa74921b9af5a0443edc45c6788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85be66eadf9e42bf682ab1d827b6ca10.png)
![](https://img.xkw.com/dksih/QBM/2016/11/22/1573167655288832/1573167661498368/STEM/0cf6f921b91a40898df3ad2dc873ba7f.png?resizew=222)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9e953a4a5f98c96bbe67cbaadf76d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6895da13331cb525f5850d7b7a02a847.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8e0c5bcf2d86726cd9f561b8ff5fe.png)
您最近一年使用:0次
2016-12-01更新
|
616次组卷
|
4卷引用:江西省景德镇一中2017-2018学年高二上学期期末考数学(理)试题
江西省景德镇一中2017-2018学年高二上学期期末考数学(理)试题(已下线)2011-2012学年浙江省温州市温州中学高三下学期第三次理科数学试卷2017届浙江温州中学高三10月高考模拟数学试卷浙江省丽水四校联考2019-2020学年高三9月阶段性考试数学试题
11-12高二下·江西上饶·期中
解题方法
2 . 如图,在正四棱柱
中,
,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/2012/4/26/1570843746656256/1570843752185856/STEM/119d6a928410411dac0d31f0d860cac6.png?resizew=217)
(Ⅰ) 证明:
平面
;
(Ⅱ)证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882dfc68c6d979b5d2b780c4a91373b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://img.xkw.com/dksih/QBM/2012/4/26/1570843746656256/1570843752185856/STEM/119d6a928410411dac0d31f0d860cac6.png?resizew=217)
(Ⅰ) 证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af142a6050b54e8b5777a085d4597481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
11-12高二下·江西赣州·阶段练习
解题方法
3 . 如图, 在直三棱柱
中,
,
,点D是AB的中点,
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429228f882da65a8e0064c88d02b8e40.png)
(2)求证:
平面
;
(3)求几何体
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c88d4954b9a1e1f3861ffa0dfef9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5eb38763ccb8cf5b582bee4a9bf3bc.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429228f882da65a8e0064c88d02b8e40.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cb62f4c1e0e023619922eb8a509c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc7e774e4ae40c23bf4ceed179230ca.png)
(3)求几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7f882a4d662fe77c87273c86de72c9.png)
.
![](https://img.xkw.com/dksih/QBM/2012/3/19/1570808860172288/1570808865710080/STEM/44db72a3428b401bb712e94d94b076c2.png?resizew=280)
您最近一年使用:0次
11-12高二下·江西赣州·周测
解题方法
4 . 在直三棱柱
中,
,
,
是
的中点,
是
上一点,且
.
(1)求证:
平面
;
(2)求三棱锥
的体积;
(3)试在
上找一点
,使得
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2066402bc6a24b56f41f9e26551e038f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60572975f9ac06ffc8d98ef94de49eb0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f94bf6140206c527ca23425ede214d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038db9ae5f76abd5c5432181eb92ad7e.png)
(3)试在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://img.xkw.com/dksih/QBM/2012/3/4/1570786788786176/1570786794201088/STEM/3254671502f44e15b4b895e875a19a66.png?resizew=190)
您最近一年使用:0次
10-11高三上·江西·期中
5 . 一个多面体的直观图和三视图如图所示,其中M、N分别是AB、AC的中点,G是DF上的一动点.
(1)求证:![](https://img.xkw.com/dksih/QBM/2010/11/18/1569907439484928/1569907444736000/STEM/7573863f138947e7b20aa16d1c641dbf.png)
(2)当FG=GD时,在棱AD上确定一点P,使得GP//平面FMC,并给出证明.
(1)求证:
![](https://img.xkw.com/dksih/QBM/2010/11/18/1569907439484928/1569907444736000/STEM/7573863f138947e7b20aa16d1c641dbf.png)
(2)当FG=GD时,在棱AD上确定一点P,使得GP//平面FMC,并给出证明.
![](https://img.xkw.com/dksih/QBM/2010/11/18/1569907439484928/1569907444736000/STEM/3cd5d5cdf7a24d5782167ad77533dc0a.png)
您最近一年使用:0次
2016-12-01更新
|
475次组卷
|
5卷引用:2011届江西省师大附中高三上学期期中考试数学文卷
(已下线)2011届江西省师大附中高三上学期期中考试数学文卷(已下线)2012届江西省师大附中高三下学期开学考试文科数学(已下线)2011-2012学年江西省白鹭洲中学高二下学期第二次月考文科数学试卷黑龙江省齐齐哈尔市克东县克东一中、克山一中等五校联考2019-2020学年高二上学期期中数学(文)试题黑龙江省齐齐哈尔市克东县克东一中、克山一中等五校联考2019-2020学年高二上学期期中数学(理)试题
2012·江西南昌·一模
名校
解题方法
6 . 如图,在三棱柱
中,侧面
底面ABC,
,且
,O为AC中点.
![](https://img.xkw.com/dksih/QBM/2012/1/16/1570692344266752/1570692349165568/STEM/b3e5b6dcbb724cfc9ac789474a590738.png?resizew=333)
(1)求直线
与平面
所成角的正弦值;
(2)在
上是否存在一点E,使得
平面
,若不存在,说明理由;若存在,确定点E的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31510125b0db45b7edef1ef444d71bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/2012/1/16/1570692344266752/1570692349165568/STEM/b3e5b6dcbb724cfc9ac789474a590738.png?resizew=333)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af142a6050b54e8b5777a085d4597481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
您最近一年使用:0次
2016-12-01更新
|
1339次组卷
|
8卷引用:2012届江西省南昌市高三调研理科数学
(已下线)2012届江西省南昌市高三调研理科数学山东省临沂市兰陵县2019-2020学年高二上学期期末数学试题人教B版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 专题强化练2 线面角及二面角的求法+专题强化练3 利用空间向量解决立体几何中的探索性问题专题1.4 空间向量与立体几何(B卷提升篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)(已下线)专题1.9 空间向量的应用-重难点题型精讲-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)重庆市第八中学校2021-2022学年高二下学期期末复习二数学试题宁夏银川市永宁县上游高级中学2023-2024学年高二上学期月考(一)数学试题宁夏回族自治区固原市彭阳县第一中学2023-2024学年高二上学期期中考试数学试题
11-12高三上·广东中山·期末
解题方法
7 . 如图,已知四棱锥
中,底面
是直角梯形,
,
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/2011/2/19/1570002572820480/1570002577965056/STEM/d09771798a7a4ecba9ba74897b2f4f47.png?resizew=228)
(1)求证:
平面
;
(2)求证:
平面
;
(3)若M是PC的中点,求三棱锥M—ACD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c3d3e9628cd503a443024410e87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.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/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://img.xkw.com/dksih/QBM/2011/2/19/1570002572820480/1570002577965056/STEM/d09771798a7a4ecba9ba74897b2f4f47.png?resizew=228)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)若M是PC的中点,求三棱锥M—ACD的体积.
您最近一年使用:0次
10-11高二下·江西上饶·阶段练习
8 . 如图,在四棱锥P-ABCD中,底面ABCD是正方形,侧棱PD
底面
,垂足为F,点E是PC的中点,
![](https://img.xkw.com/dksih/QBM/2011/4/1/1576739822256128/1576739876249600/STEM/05390f79f1be4e88aa05699749308118.png?resizew=178)
(1)求证:PA∥平面BDE;
(2)求证:PB⊥平面DEF;
(3)求二面角B—DE—F的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e726b3e53a7c4f5bced2d785213d24c4.png)
![](https://img.xkw.com/dksih/QBM/2011/4/1/1576739822256128/1576739876249600/STEM/05390f79f1be4e88aa05699749308118.png?resizew=178)
(1)求证:PA∥平面BDE;
(2)求证:PB⊥平面DEF;
(3)求二面角B—DE—F的余弦值.
您最近一年使用:0次
9 . 如图所示, 在直三棱柱ABC-A1B1C1中,AC=3,BC=4,AB=5,AA1=4,点D是AB的中点,
(1)求证: AC1//平面CDB1;
(2)求二面角C1-AB-C的平面角的正切值.
(1)求证: AC1//平面CDB1;
(2)求二面角C1-AB-C的平面角的正切值.
![](https://img.xkw.com/dksih/QBM/2012/3/8/1570792093155328/1570792098365440/STEM/4911972024434e6f94886f778f95c22a.png?resizew=189)
您最近一年使用:0次
2016-12-01更新
|
523次组卷
|
4卷引用:江西省南昌市进贤县第一中学2019-2020学年高二下学期开学考试数学(理)试题
江西省南昌市进贤县第一中学2019-2020学年高二下学期开学考试数学(理)试题(已下线)2012届湖南省衡阳市八中高三第四次月考文科数学(已下线)2012届湖南省郴州市一中高三下学期第六次月考文科数学重庆两江新区西南大学附属中学2021-2022学年高二上学期开学考试数学试题
10 . 如图,在直三棱柱ABC-A1B1C1中,∠BAC=90°,AB=AC=AA1=1,延长A1C1至点P,使C1P=A1C1,连接AP交棱CC1于D.
![](https://img.xkw.com/dksih/QBM/2011/6/30/1570249076563968/1570249081831424/STEM/01360ac5-78ef-4896-b8bd-6d5a8137e297.png?resizew=200)
(1)求证:PB1//平面BDA1;
(2)求二面角A-A1D-B的平面角的余弦值.
![](https://img.xkw.com/dksih/QBM/2011/6/30/1570249076563968/1570249081831424/STEM/01360ac5-78ef-4896-b8bd-6d5a8137e297.png?resizew=200)
(1)求证:PB1//平面BDA1;
(2)求二面角A-A1D-B的平面角的余弦值.
您最近一年使用:0次
2016-11-30更新
|
1325次组卷
|
5卷引用:江西省宜春市樟树中学2017-2018学年高二下学期第三次月考数学(理)试题