名校
解题方法
1 . 如图,在边长为8的菱形
中,
,点
,
分别是边
,
的四等分点,
,
,
,
交于
点,沿
将
翻折到
,连接
,
,
,得到如图的五棱锥
,且
与底面
所成角的正弦值为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/49f20280-f89c-41e9-a847-f91d25f87096.png?resizew=464)
(1)求证:
平面
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b7ff28dbeeedec243fc8eb7cb5d368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc68246c6e5502b67fbcf3583dafe019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cbcc0e404e813f42bad22853220347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b7b2c0db9c5c5c0c82d3fa62bf5e5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafd8ea63ced193942ba59fcb24ae73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11682da72980dde9834ba91c3d995e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/49f20280-f89c-41e9-a847-f91d25f87096.png?resizew=464)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83efd6afec2f73c52e4b027a12d9f817.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a43c429d2676774d09e2509d9e26a0d.png)
您最近一年使用:0次
2 . 如图,在三棱柱
中,
,底面为正三角形,
,D是BC的中点,P是
的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/5b9c3d48-2d88-42ad-91a8-252d8cbf26cd.png?resizew=124)
(1)
平面
;
(2)
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc61a2aa5d8aebe6773d235f31ed81f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa3d0db9ad31d33c2883a6efed1dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/5b9c3d48-2d88-42ad-91a8-252d8cbf26cd.png?resizew=124)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896e293411e2fd0da215ff20781cb36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c823e54bf3a3a7f1916a4886eb6279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
您最近一年使用:0次
2020-01-14更新
|
201次组卷
|
3卷引用:湖北省恩施州利川市第五中学2020-2021学年高二上学期期中数学试题
名校
解题方法
3 . 如图,在四棱柱
中,
平面
,底面ABCD满足
∥BC,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effdeab01e845277aa6f1c1475fb7640.png)
![](https://img.xkw.com/dksih/QBM/2020/4/5/2435008730226688/2435850537476096/STEM/a83af5db-7185-4eec-b7b0-adb91ab5daa1.png)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effdeab01e845277aa6f1c1475fb7640.png)
![](https://img.xkw.com/dksih/QBM/2020/4/5/2435008730226688/2435850537476096/STEM/a83af5db-7185-4eec-b7b0-adb91ab5daa1.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
您最近一年使用:0次
2020-04-06更新
|
1520次组卷
|
21卷引用:2020届北京市西城区高三第一次模拟考试数学试题
2020届北京市西城区高三第一次模拟考试数学试题2020届宁夏石嘴山市高三4月二模数学(理)试题(已下线)专题04 立体几何-2020年高三数学(理)3-4月模拟试题汇编陕西省渭南市韩城市2020届高三(6月份)高考数学(理科)模拟试卷宁夏石嘴山市2020届高三适应性测试数学(理)试题(已下线)专题16 立体几何-2020年高考数学母题题源解密(北京专版)(已下线)专题18 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅰ专版)(已下线)专题8.9 空间向量与立体几何单元测试卷-2021年新高考数学一轮复习学与练湖北省鄂州市2021-2022学年高二上学期期末数学试题陕西省汉中市2021届高三上学期第一次校际联考理科数学试题重庆市万州第二高级中学2021-2022学年高二上学期第一次月考数学试题山东省济宁市邹城市第二中学2021-2022学年高二上学期10月月考数学试题黑龙江省大庆市大庆铁人中学2021-2022学年高二上学期第一次月考数学试题北京市房山区良乡中学2022届高三上学期期中考试数学试题湖南省邵阳市邵东市第一中学2021-2022学年高二上学期期中数学试题陕西省安康市2021-2022学年高二下学期期末理科数学试题河北省石家庄市二十三中2022-2023学年高二上学期第一次月考数学试题陕西省榆林市绥德中学2023届高三上学期第二次模拟考试理科数学试题浙江省绍兴蕺山外国语学校2022-2023学年高二上学期10月检测数学试题福建省永安市第九中学2022-2023学年高二上学期9月月考数学试题河南省洛阳市新安县第一高级中学2022-2023学年高二上学期9月月考数学试题
名校
4 . 在四棱柱
中,已知底面
是边长为
的菱形,且
.
(1)证明:
平面
;
(2)若
,
,且该四棱柱的体积为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56968a985f7698e4348e3b1167f107.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc1c04946340198af69170d4ebd4b42.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d283a0744146ad9cf24edddbc46501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/5cf36e66-7ef5-4b73-8a27-989443f0b7ff.png?resizew=205)
您最近一年使用:0次
5 . 如图,长方体ABCD﹣A1B1C1D1中,AB=AD=1,AA1=2,点P为DD1的中点,点M为BB1的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/9eb15769-6e3d-49e1-a01a-b740de22e6ee.png?resizew=130)
(1)求证:PB1⊥平面PAC;
(2)求直线CM与平面PAC所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/9eb15769-6e3d-49e1-a01a-b740de22e6ee.png?resizew=130)
(1)求证:PB1⊥平面PAC;
(2)求直线CM与平面PAC所成角的正弦值.
您最近一年使用:0次
2020-01-11更新
|
252次组卷
|
3卷引用:湖北省黄石市2018-2019学年高二上学期期末质量监测考试数学(理)试题
名校
解题方法
6 . 如图在四棱锥
中,平面
底面ABCD,底面ABCD是等腰梯形,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
.
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480342232137728/2480701720436736/STEM/9dde8ca597b34fdabdb928ae2b5dd6f1.png?resizew=168)
(1)证明:
.
(2)求平面PCD与平面PAB夹角(锐角)的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab40c3da31f132ceded9671f5020ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a0c299356c26338d4153748e8a61d.png)
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480342232137728/2480701720436736/STEM/9dde8ca597b34fdabdb928ae2b5dd6f1.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c231fb9aeaf4b73c2d835bb4c3d42b.png)
(2)求平面PCD与平面PAB夹角(锐角)的余弦值.
您最近一年使用:0次
2020-06-09更新
|
455次组卷
|
3卷引用:湖北省荆门市龙泉中学2020届高三下学期高考适应性考试(二)数学(理)试题
名校
7 . 如图,直三棱柱
中,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
平面
;
(2)已知
与平面
所成的角为30°,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.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/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319d234a0586478d4e73020d48b3a10.png)
您最近一年使用:0次
2020-05-13更新
|
2757次组卷
|
16卷引用:湖北省襄阳市2019-2020学年高二上学期期末数学试题
湖北省襄阳市2019-2020学年高二上学期期末数学试题湖北省宜昌市天问高中2019-2020学年高二(下)开学数学试题【市级联考】辽宁省丹东市2019届高三总复习质量测试(一)理科数学试题四川省广安市广安中学2019-2020学年高二9月月考(文)数学试题黑龙江省鹤岗市第一中学2019-2020学年高三上学期10月月考数学(理)试题江西省吉安市2019-2020学年高三上学期期中数学(理)试题江西省宜春市上高县第二中学2019-2020学年高三上学期11月月考数学(理)试题2020届河北省衡水中学高三年级上学期五调考试数学(理科)试题2020届黑龙江省实验中学高三上学期期末考试数学(理)试题四川省棠湖中学2019-2020学年高三下学期第二次月考数学(理)试题(已下线)专题01 平行、垂直问题的证明(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖山东济南市历城第二中学2019-2020学年高一下学期开学考试数学试题江苏省无锡市江阴市高级中学2019-2020学年高二下学期期中数学试题2020届河北省衡水中学高三高考考前密卷(一)数学(理)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 1.2 空间向量在立体几何中的应用 1.2.4 二面角甘肃省永昌县第一中学2020-2021学年高三上学期第一次月考数学理试题
名校
8 . 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
9 . 如图,在四棱柱
中,底面ABCD是等腰梯形,
,
,
,顶点
在底面ABCD内的射影恰为点C.
![](https://img.xkw.com/dksih/QBM/2020/3/24/2426683543445504/2426969450962944/STEM/449b5ed97f83408886aba846afb04e0a.png?resizew=198)
(1)求证:BC⊥平面ACD1;
(2)若直线DD1与底面ABCD所成的角为
,求平面
与平面ABCD所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://img.xkw.com/dksih/QBM/2020/3/24/2426683543445504/2426969450962944/STEM/449b5ed97f83408886aba846afb04e0a.png?resizew=198)
(1)求证:BC⊥平面ACD1;
(2)若直线DD1与底面ABCD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
您最近一年使用:0次
2020-03-25更新
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288次组卷
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4卷引用:湖北省孝感市应城市第一高级中学2019-2020学年高二下学期期中数学试题
10 . 如图,在四棱台ABCD-A1B1C1D1中,底面ABCD是菱形,∠ABC=
,∠B1BD=
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58df8d911935cca1738567b656c8e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41430e9e5f22c2330333613390612fb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/4ee63947-6239-496a-88ad-5660c468f68e.png?resizew=179)
(1)求证:直线AC⊥平面BDB1;
(2)求直线A1B1与平面ACC1所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58df8d911935cca1738567b656c8e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41430e9e5f22c2330333613390612fb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/4ee63947-6239-496a-88ad-5660c468f68e.png?resizew=179)
(1)求证:直线AC⊥平面BDB1;
(2)求直线A1B1与平面ACC1所成角的正弦值.
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2020-03-19更新
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10卷引用:2020届浙江省名校协作体高三下学期3月第二次联考数学试题
2020届浙江省名校协作体高三下学期3月第二次联考数学试题安徽省合肥一中2020-2021学年高二上学期10月段考数学(理)试题湖北省九校教研协作体2022-2023学年高二上学期9月联考数学试题湖北省温德克英联盟2023-2024学年高二8月开学综合性难度选拔考试数学试题山东省齐鲁2021-2022学年3月份高一阶段性质量检测试卷A福建省福州格致中学2022届高三数学模拟试题(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-2广东省中山市2023-2024学年高二上学期期末统一考试数学试题2024年全国普通高中九省联考仿真模拟数学试题(三)湖南省岳阳市第一中学2023-2024学年高三下学期开学考试数学试题