名校
解题方法
1 . 在三棱锥
中,
底面ABE,AB⊥AE,
,D是AE的中点,C是线段BE上的一点,且
,连接PC,PD,CD.
![](https://img.xkw.com/dksih/QBM/2021/12/9/2868928959971328/2946617072418816/STEM/a4516363-2f77-4478-907b-4eacfe376dba.png?resizew=178)
(1)求证:
平面PAB;
(2)求点E到平面PCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca19321c6776be24e4be5033b60ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb241abc97d26f1c693c53acb7c64cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62eccb33ea66c03222468628f74d8c56.png)
![](https://img.xkw.com/dksih/QBM/2021/12/9/2868928959971328/2946617072418816/STEM/a4516363-2f77-4478-907b-4eacfe376dba.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dace90bcafd1fbf25f272b05c3875f6.png)
(2)求点E到平面PCD的距离.
您最近一年使用:0次
2022-03-29更新
|
1944次组卷
|
14卷引用:【全国市级联考】湖南省益阳市2018届高三4月调研考试数学(文)试题
【全国市级联考】湖南省益阳市2018届高三4月调研考试数学(文)试题【全国百强校】宁夏石嘴山市第三中学2018届高三下学期第四次模拟考试数学(文)试题河南省郑州市第一中学2019届高三高考适应性考试数学(文)试题河北省石家庄市辛集市中学2019-2020学年高三第三次月考数学(文)试题湖南省长沙市宁乡一中2018-2019学年高三上学期10月月考文科数学试题四川省泸州市泸县第四中学2019-2020学年高二下学期期中考试数学(文)试题安徽省合肥市第七中学2020-2021学年高二上学期期中理科数学试题四川省泸州市泸县第四中学2022届高三三诊模拟考试文科数学试题广东省北京师范大学珠海分校附属外国语学校2021-2022学年高一下学期期中数学试题(已下线)第8章 立体几何初步 章末综合检测 -2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)(已下线)必刷卷03(文)-2022年高考数学考前信息必刷卷(全国甲卷)山西省太原师范学院附属中学、太原市师苑中学校2021-2022学年高一下学期第四次联考数学试题广东省东莞市东莞外国语学校2021-2022学年高一下学期期中数学试题(已下线)第07讲 立体几何大题(11个必刷考点)-《考点·题型·密卷》
名校
解题方法
2 . 如图在四棱锥
中,
,
,
,
,
.
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/26/2708333832388608/2786526973804544/STEM/881a9c07-9d3e-49ba-a041-50fb4069481e.png?resizew=209)
(1)求证:
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de728cae820b49ee7164cdbe600bdc92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8216185daba3b3d58e4b6ee6c579f006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a6c501e8522d47051f0dd296e427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43951dba3f9f8548c47bf6f26d58f17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/2021/4/26/2708333832388608/2786526973804544/STEM/881a9c07-9d3e-49ba-a041-50fb4069481e.png?resizew=209)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e68cd41f4d22e9b05ab846af585a0e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2021-08-15更新
|
501次组卷
|
4卷引用:湖南省益阳市桃江县第四中学2023-2024学年高二下学期3月月考数学试题
3 . 如图,四棱台ABCD﹣A1B1C1D1中,A1A⊥平面ABCD,底面ABCD是平行四边形,∠ABC=
,BC=
AB=2
,A1B1=A1A=1.
平面ACB1;
(2)求二面角A﹣B1C﹣D1的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)求二面角A﹣B1C﹣D1的余弦值.
您最近一年使用:0次
2021-05-02更新
|
616次组卷
|
4卷引用:湖南省益阳市2021届高三下学期4月高考模拟数学试题
湖南省益阳市2021届高三下学期4月高考模拟数学试题广东省佛山市萌茵2021届高三高考数学适应性试题(已下线)第20题 立体几何解答题的两大主题:线面位置的证明及空间角-2021年高考数学真题逐题揭秘与以例及类(新高考全国Ⅰ卷)(已下线)专题3.6 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)
名校
4 . 如图,在四棱锥
中,二面角
是直二面角,
为等腰直角三角形
的斜边,
,
,
,
为线段
上的动点.
![](https://img.xkw.com/dksih/QBM/2021/3/11/2675600314425344/2683955655827456/STEM/bee3ad803b084a24be82a16ff65228bf.png?resizew=235)
(1)当
时,证明:
平面
;
(2)若平面
平面
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d399d731913a563e291b817831a0c678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af633abfe3cb03f1836db6c570a5bcc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2021/3/11/2675600314425344/2683955655827456/STEM/bee3ad803b084a24be82a16ff65228bf.png?resizew=235)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6e349d06e669d2e02ecbc69f6bb9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fb16d2f0db758b8b7a8d3743143f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c7f31a3c7724e968a7dd08652bc4f4.png)
您最近一年使用:0次
2021-03-23更新
|
725次组卷
|
4卷引用:湖南省益阳市安化县第二中学2023届高三下学期模拟考试数学试题
5 . 如图,在长方体
中.
![](https://img.xkw.com/dksih/QBM/2020/7/24/2512860608864256/2512977270177792/STEM/871c0a7b-ce7a-4bdb-b0ea-0d41cc5b0661.png)
(1)求证:
平面
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2020/7/24/2512860608864256/2512977270177792/STEM/871c0a7b-ce7a-4bdb-b0ea-0d41cc5b0661.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc3f049152c43dd29b12d0a60aa79f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0b24d3b14c326b2baa2d2c5e8db871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
6 . 如图所示的几何体中,正方形
与梯形
所在的平面互相垂直,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/0bd03940-0186-45c7-98c8-cc184741b45f.png?resizew=155)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求二面角
的余弦值.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/0bd03940-0186-45c7-98c8-cc184741b45f.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b820c84570da9c38d0a81c22788b76.png)
您最近一年使用:0次
7 . 如图,在三棱锥
中,
,
,D,E分别为BC,PD的中点,F为AB上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/44516335-29bd-4f3f-8cf7-6e7e0ba6a14b.png?resizew=172)
(1)求证:
平面PAD;
(2)求证:
平面PAC;
(3)若二面角
为60°,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a22cfb2c0d21594431303d06b30cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209377196940bffa8ffa5f55b9c59fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d318ccd750364557b52b8e2fd9e47eb0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/44516335-29bd-4f3f-8cf7-6e7e0ba6a14b.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16835e3f230ba3f543b6804e445e283.png)
(3)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
8 . 如图,在四棱锥
中,底面ABCD为矩形,O,E分别为AD,PB的中点,平面
平面ABCD,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/95681eae-26de-4a54-8f34-70c462101995.png?resizew=212)
(1)求证:
平面PCD;
(2)求证:
平面PCD;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc28e69c1ba0aac981256887f7dfa94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/95681eae-26de-4a54-8f34-70c462101995.png?resizew=212)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af142a6050b54e8b5777a085d4597481.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6a0cee8226e82cc57916e10d533369.png)
您最近一年使用:0次
9 . 如图1所示,在直角梯形DCEF中,
,
,
,
,将四边形ABEF沿AB边折成图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/aec2c5b1-e4ae-47a6-88e4-3768ce614599.png?resizew=284)
(1)求证:
平面DEF;
(2)若
,求平面DEF与平面EAC所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e2460c7fcab438184216179e6b1ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed15bdc3e6739ed2cb4590fa44246c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d950ad1d861fa6fd64b7147ebb9c413e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/aec2c5b1-e4ae-47a6-88e4-3768ce614599.png?resizew=284)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c233b95865198572282d7a66ce689e94.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edbb7850e42abf006017b477d85dee5.png)
您最近一年使用:0次
2020-01-28更新
|
414次组卷
|
2卷引用:2020届湖南省益阳市高三上学期期末数学(理)试题