名校
1 . 如图所示,四边形
为菱形,
,平面
平面
,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/11/c44bd8a6-5ee1-409d-a506-0e63aadc7395.png?resizew=169)
(1)求证:
;
(2)若
,求三棱锥
的体积.
(3)若
,当二面角
的正切值为
时,求直线
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/11/c44bd8a6-5ee1-409d-a506-0e63aadc7395.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc56fdf70e65bd88980c64af96b83da.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b1fa95e2d4cff19c511e77ad83eabd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0199f36fcea2e8321aba196ec9cb8de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-02-05更新
|
1600次组卷
|
8卷引用:河南省洛阳复兴学校2021-2022学年高一下学期5月月考数学试题
河南省洛阳复兴学校2021-2022学年高一下学期5月月考数学试题 (已下线)8.6.3 平面与平面垂直(2)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)期中考试测试(提升)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)第19讲 空间图形的表面积和体积吉林省普通高中友好学校第三十六届联合体2022-2023学年高一下学期期中联考数学试题(已下线)专题强化二:异面角、线面角、二面角的常见解法 (2)福建省三明市永安第九中学2022-2023学年高一下学期5月月考数学试题
2 . 如图,正方体
的棱长为2,若点
在线段
上(不含端点)运动,则下列结论正确的为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/25/e795298d-5d2f-4909-b105-8862831e095c.png?resizew=174)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/25/e795298d-5d2f-4909-b105-8862831e095c.png?resizew=174)
A.直线![]() ![]() |
B.三棱锥![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2023-01-20更新
|
1411次组卷
|
7卷引用:广东省广州市天河区2023届高三二模数学试题
(已下线)广东省广州市天河区2023届高三二模数学试题(已下线)江苏省盐城市、南京市2022届高三上学期1月第一次模拟考试数学试题变式题11-16山西省朔州市怀仁市2023届高三二模数学试题专题15空间向量与立体几何(多选题)(已下线)考点17 立体几何中的定值问题 2024届高考数学考点总动员【练】(已下线) 第1章 空间向量与立体几何单元测试能力卷-2023-2024学年高二数学上学期人教A版(2019)选择性必修第一册广东省深圳市南山区2023届高三上学期期末数学试题
解题方法
3 . 正四面体
中,
是侧棱
上(端点除外)的一点,若异面直线
与直线
所成的角为
,直线
与平面
所成的角为
,二面角
的平面角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70682f6196e6c1a08eb48da73e8919ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
4 . 在直四棱柱
中,底面
为直角梯形,
,点M在该四棱柱表面上运动,且满足平面
平面
.当线段
的长度取到最大值时,直线
与底面
所成角的正弦值是( )
![](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/d9d4643f7a0c30189e6bb826fdafcc8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d42ef49f3facd3ae86960d2f81e52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9a248d1d22e1c29cfbce96b32e2206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 如图,已知四棱锥
的底面是平行四边形,侧面
是等边三角形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/b510fd31-7d97-494b-bd42-8723be2d1901.png?resizew=269)
(1)求
与平面
所成角的正弦值;
(2)设
为侧棱
上一点,四边形
是过
两点的截面,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
平面
,是否存在点
,使得平面
平面
?若存在,求出点
的位置;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a0962d12261a67e66a6bc94fbb5f37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/b510fd31-7d97-494b-bd42-8723be2d1901.png?resizew=269)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea65669073300fd1a05649c0a99b41b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fec6396b390bffbcb0fd26abee5d7e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea65669073300fd1a05649c0a99b41b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43324af1da8a28dc0fceb5e3e87617a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
6 . 如图,在三棱柱
中,
为
的中点,
为等边三角形,直线
与平面
所成角大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/c803964d-228d-49cc-ad12-cff4a2216289.png?resizew=246)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408b3698a4cca4c4fd4396e62542b66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/c803964d-228d-49cc-ad12-cff4a2216289.png?resizew=246)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e46fca7d5918b0572984aa3143f182a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2022-12-09更新
|
2912次组卷
|
7卷引用:山西省运城市景胜中学2023届高三上学期12月月考数学试题
山西省运城市景胜中学2023届高三上学期12月月考数学试题河南省南阳市2022-2023学年高三第二次大练习数学(理)试题河南省五市2023届高三第一次联考数学(理科)试题2023届四川省名校联考高考仿真测试(五)理科数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-192024届高三新高考改革数学适应性练习(一)(九省联考题型)湖北省十一校2023届高三上学期12月第一次联考数学试题
2022·全国·模拟预测
名校
解题方法
7 . 如图1,在菱形ABCD中,
,
,将
沿AC折起,使点B到达点P的位置,形成三棱锥
,如图2.在翻折的过程中,下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/1273fe8f-dd95-49e3-b6b8-ef57dc2af275.png?resizew=324)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c482ee1668a59ca21f3ae8b6bad58eae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/1273fe8f-dd95-49e3-b6b8-ef57dc2af275.png?resizew=324)
A.![]() |
B.三棱锥![]() |
C.存在某个位置,使![]() |
D.若平面![]() ![]() |
您最近一年使用:0次
名校
8 . 如图,在平行四边形
中,
,
分别为
的中点,沿
将
折起到
的位置(
不在平面
上),在折起过程中,下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9bba30fadf42ba865a15f4a000da37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df7fc746f8c4801d8f2f0471ba3297e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cde52e02168c74b4b1c0a8ce09287df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若![]() ![]() ![]() ![]() |
B.存在某位置,使![]() |
C.当二面角![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2022-11-30更新
|
1599次组卷
|
8卷引用:黑龙江省哈尔滨市第三中学校2022-2023学年高三上学期阶段性测试(三)数学试题
名校
解题方法
9 . 在长方体
中.
,
,
是线段
上的一动点,如下的四个命题中,
(1)
平面
;
(2)
与平面
所成角的正切值的最大值是
;
(3)
的最小值为
;
(4)以
为球心,
为半径的球面与侧面
的交线长是
.
真命题共有几个( )
![](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/0d8772aa893a9c1d40f714cb25701701.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f86e2d69b11402d9d6cbb06e057778a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57132b0bd38c035fec010ee3be1bc8fe.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138e0045398b0f40258ae51abe8b6f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63c1f30aa78aada181a0923b6c1c69e.png)
(4)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5170e87322172ef27379adb171d4b76e.png)
真命题共有几个( )
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2022-11-10更新
|
540次组卷
|
3卷引用:四川省泸州市叙永第一中学校2022-2023学年高二上学期第一学月教学质量检测数学(理)试题
四川省泸州市叙永第一中学校2022-2023学年高二上学期第一学月教学质量检测数学(理)试题四川省广安市第二中学校2022-2023学年高二下学期第一次月考数学(理)试题(已下线)专题8.18 立体几何初步全章综合测试卷(提高篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
解题方法
10 . 如图,在长方体
中,
,点E为棱BC上靠近点C的三等分点,点F是长方形
内一动点(含边界),且直线
,EF与平面
所成角的大小相等,则下列说法错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/6/7e817a3b-039d-4b50-9beb-17f4f79d987f.png?resizew=175)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1baa492b87c78b80b9a58e24e67fc50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc725182c2fd1413319fea35b95c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/6/7e817a3b-039d-4b50-9beb-17f4f79d987f.png?resizew=175)
A.![]() ![]() | B.三棱锥![]() |
C.存在点F,使得![]() | D.线段![]() ![]() |
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2022-11-05更新
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853次组卷
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3卷引用:安徽省亳州市2020-2021学年高一上学期期末数学试题