解题方法
1 . 如图,四棱锥中,底面是边长为2的正方形,
是以
为斜边的等腰直角三角形,
平面
,点
是线段
上的中点,
是
的中点.
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
2 . 如图,在四棱锥
中,四边形
是菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/f3a6b22b-d1a0-40f1-9c9c-6ffb655cd8cd.png?resizew=170)
(1)证明:平面
平面
.
(2)求二面角
的余弦值.
![](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/917059c4d68de6935b5b010edd3b2efb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/f3a6b22b-d1a0-40f1-9c9c-6ffb655cd8cd.png?resizew=170)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b31c44f920e6e09b02f03ec82ef843.png)
您最近一年使用:0次
2024-03-03更新
|
454次组卷
|
2卷引用:贵州省黔东南苗族侗族自治州2023-2024学年高三上学期九校联考(开学考)数学试题
3 . 如图①所示,在
中,
,
,
,
垂直平分
.现将
沿
折起,使得二面角
的大小为
,得到如图②所示的四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/7274ba83-6c0c-4082-bcf5-510d929f6bb6.png?resizew=272)
(1)求证:平面
平面
;
(2)若Q为
上一动点,且
,当锐二面角
的余弦值为
时,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10072660396c4821badfd7311389e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370148e9147aa25c60a07ab4ad46e83d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede9e40f5cf450db6f01194559a19c7e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/7274ba83-6c0c-4082-bcf5-510d929f6bb6.png?resizew=272)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
(2)若Q为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7c856cacd405be26cba2acfeeb921e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992f6109277b1d72fe1057ba9052a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27334f60a230aa3f5bc5365e55f53c1.png)
您最近一年使用:0次
2023-12-24更新
|
352次组卷
|
3卷引用:贵州省铜仁第一中学2023-2024学年高二下学期2月开学适应性模拟检测数学试题
解题方法
4 . 如图,在四棱台
中,底面为矩形,平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/efb8c393-3bf3-4f29-8029-dfd87a376fe9.png?resizew=202)
(1)证明:
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795c38ba0cdec1de7d67c20d9e9fb338.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/efb8c393-3bf3-4f29-8029-dfd87a376fe9.png?resizew=202)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d90f7b3d321961d3c1b8e25ba56f03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc1c04946340198af69170d4ebd4b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-10-19更新
|
160次组卷
|
3卷引用:贵州省“三新“”改革联盟2023-2024学年高二上学期第一次联考数学试题
解题方法
5 . 如图1平行四边形
由一个边长为6的正方形和2个等腰直角三角形组成,沿
将2个三角形折起到与平面
垂直(如图2),连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980873ea60dbb6a7ef8b1885b849578d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/006b4ac8-cfc8-495e-8d1e-ca9573fbba00.png?resizew=353)
(1)求点E到平面
的距离;
(2)线段
上是否存在点M,使得直线
与平面
的夹角为30°.若存在,指出点M的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980873ea60dbb6a7ef8b1885b849578d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/006b4ac8-cfc8-495e-8d1e-ca9573fbba00.png?resizew=353)
(1)求点E到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
您最近一年使用:0次
2023-10-19更新
|
226次组卷
|
2卷引用:贵州省“三新“”改革联盟2023-2024学年高二上学期第一次联考数学试题
6 . 如图所示,在平行六面体
中,
,
分别在
和
上,且
.
(1)证明
四点共面;
(2)若
与
相交与点
,求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead0e8eadfdcefa334953e88864f424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28efb60d0c7a8642064d696624d98a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009e03ffd0b0ec7a287482683636782e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/7/0d6ab5c3-8c0b-454f-80cc-da3400317fd6.png?resizew=169)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c26c8c134dcd26fc0e7f39774db5f9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-10-19更新
|
208次组卷
|
2卷引用:贵州省“三新“”改革联盟2023-2024学年高二上学期第一次联考数学试题
名校
7 . 如图,是正三角形,四边形
是矩形,平面
平面
,
平面
,点
为
中点,
,
.
(1)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c29f3123f57b56444be9bc048eacc82.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd33fee392c7acf212ccdd35a9cd5b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fecaad729e54dc1c9cea29c27d362b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2023-09-10更新
|
744次组卷
|
5卷引用:贵州省贵阳市2024届高三上学期8月摸底考试数学试题
贵州省贵阳市2024届高三上学期8月摸底考试数学试题河南省郑州市郑州外国语学校2023-2024学年高二上学期10月月考数学试题(已下线)第七章 综合测试A(基础卷)(已下线)专题09 空间距离与角度8种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)(已下线)通关练03 用空间向量解决距离、夹角问题10考点精练(58题) - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
名校
解题方法
8 . 如图,四棱柱
的底面
为矩形,
为
中点,平面
平面
,
且
.
(1)证明:
;
(2)若此四棱柱的体积为2,求二面角
的正弦值.
![](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/8e5e29ca242ec45e8932247be58c633a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41884a12fb840aff6012fe78e5ac2fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff7ce58deed5cf5c76fd122e9afecfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b89cfab4ace9f1ecb5f95a524225d2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/24/0bfc5c70-830a-4ed2-9ae7-8bc24324f08e.png?resizew=173)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796b217753ddf3e7616b534b624fea27.png)
(2)若此四棱柱的体积为2,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff420795b334c9934c366b99507d0026.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,直四棱柱
的底面
为菱形,且
,
,E,F分别为BC,
的中点.
(1)证明:平面
平面
.
(2)求平面
和平面
的夹角的余弦值.
![](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/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/14/37f6ef40-4402-4068-b921-e8cdb5940710.png?resizew=175)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f965d1d2bf1e3a2be2048fc379ac9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb3f0b5d8bf98eeff66f43b7dcbb4be.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1f68454096da710903e9693c7f2015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
您最近一年使用:0次
2023-08-13更新
|
845次组卷
|
4卷引用:贵州省2024届高三上学期入学考试数学试题
贵州省2024届高三上学期入学考试数学试题江西省萍乡市安源中学2022-2023学年高二下学期期末考试数学试题(已下线)第七章 立体几何与空间向量(测试)(已下线)通关练03 用空间向量解决距离、夹角问题10考点精练(58题) - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
名校
解题方法
10 . 如图,在直三棱柱
中,
,点
为
上一点,且
平面
.
![](https://img.xkw.com/dksih/QBM/2023/5/31/3249535718957056/3298264834449408/STEM/65f896cbdcd64b16ac0456b61e035af4.png?resizew=160)
(1)求
的值;
(2)若三棱锥
的体积为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64cabc69fb1e437b50acdbf43e60306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896e293411e2fd0da215ff20781cb36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
![](https://img.xkw.com/dksih/QBM/2023/5/31/3249535718957056/3298264834449408/STEM/65f896cbdcd64b16ac0456b61e035af4.png?resizew=160)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b70ff4d92d1fbda025816f88e63478a.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bb4f21d1699d81097b3934ebc2acb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fbbc8f521edab89a7e373287bcfbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
您最近一年使用:0次
2023-08-08更新
|
565次组卷
|
3卷引用:贵州省贵阳市第一中学2024届高三上学期开学考试(8月月考)数学试题