解题方法
1 . 如图①,在直角梯形ABCD中,AB∥CD,∠BAD=90°,点E为线段AB上异于A,B的点,点F为线段CD上异于C,D的点,且EF∥DA,沿EF将面EBCF折起,如图②,则下列结论正确的是( )
A.AB//CD |
B.AB//平面DFC |
C.A,B,C,D四点共面 |
D.CE与DF所成的角为直角 |
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解题方法
2 . 如图,在四棱锥
中,底面ABCD为直角梯形,其中
,
,
,
,
平面ABCD,且
,点M在棱PD上(不包括端点),点N为BC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/58a3313c-5afd-4bba-9105-98d94ac71622.png?resizew=192)
(1)若
,求证:直线
平面PAB;
(2)已知点M满足
,求异面直线MN与AD所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78dc13bf23fca088f25a71bad6708b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/58a3313c-5afd-4bba-9105-98d94ac71622.png?resizew=192)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9bd172fcd1e1a0cc8abe35b81e27c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
(2)已知点M满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4e89f22c7860dea61b26b32926cae.png)
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3卷引用: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)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)四川省成都市第七中学2022-2023学年高三下学期入学考试数学(文)试题重庆市南岸南坪中学校2022-2023学年高一下学期期中数学试题
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3 . 已知正四棱锥
的所有棱长均为
,
,
分别是
,
的中点,
为棱
上异于
,
的一动点,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804c767ba8ba0ac1fc157fc345cea965.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/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.异面直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.![]() ![]() |
D.存在点![]() ![]() ![]() |
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8卷引用:专题8.12 空间直线、平面的垂直(一)(重难点题型检测)-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)专题8.12 空间直线、平面的垂直(一)(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)湖南省四大名校名师团队2023届高三普通高校招生统一考试数学模拟冲刺卷(一)浙江省杭州第二中学2023届高三下学期3月月考数学试题山东省淄博实验中学、淄博齐盛高中2022-2023学年高三下学期3月阶段性诊断检测数学试题广东省佛山市南海区华南师范大学附属中学南海实验高级中学2023届高三保温考数学试题湖南省怀化市长沙市长郡中学等3校2023届高三上学期开学考试数学试题(已下线)专题09 立体几何初步福建省厦门第一中学2023届高三二模数学试题
解题方法
4 . 如图,在棱长为2的正四面体(四个面都是正三角形)ABCD中,M、N分别是AD、BC的中点,则异面直线AN,CM所成角的余弦值为_________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/4247b873-6094-437c-b528-8ba43cc34d07.png?resizew=156)
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4卷引用:专题8.8 空间点、直线、平面之间的位置关系(重难点题型检测)-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)专题8.8 空间点、直线、平面之间的位置关系(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)广东省广州市天河区2022-2023学年高二上学期期末数学试题广东省广州市天河区2022-2023学年高二下学期开学考数学试题(已下线)重难点专题02 空间点直线平面之间的位置关系-【同步题型讲义】
5 . 如图,梯形
中,
,
,
,沿对角线
将
折起,使点B在平面
内的投影O恰在
上.
(1)求证:
平面
;
(2)求异面直线
与
所成的角;
(3)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4182c37d2bad62dda4f901432ef9482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/7bdaa6fc-5a15-4c24-a8e7-e00e68922fec.png?resizew=322)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29cc627d76412c236aac6b29fa0fdf.png)
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解题方法
6 . 如图,在四棱锥
中,四边形
是正方形,
平面
,E是棱
的中点,则异面直线
与
所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/524ca8b7-c350-496e-afa1-2c00266b4b7f.png?resizew=154)
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181c84766862354d0df023fb85a72373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/524ca8b7-c350-496e-afa1-2c00266b4b7f.png?resizew=154)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 如图所示,在棱长为a的四面体中,E、F分别为CB、AD的中点,求DE与BF所成的角.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/739a1acd-eae3-40a6-9b3e-fe7c7606c2d1.png?resizew=142)
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8 . 体积为
的正三棱柱
中,
与
所成角大小等于
,则
与
所成角大小为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
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解题方法
9 . 圆柱的上底半径OA与下底半径
垂直,若
,AB与
所成的角为
,则AB的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913d2a71d4012f2e38a2fc3a1d33d389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
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10 . 如图,圆柱的高为4cm,底面半径为3cm,已知上底面一条半径OA与下底面的一条半径
成
角,求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/773666ff-efac-4c4b-8a7a-e389b58fbe17.png?resizew=121)
(1)直线
与圆柱的轴
所成的角的大小;
(2)线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98aa37f51ecc4c191a0b602162e69ec8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/773666ff-efac-4c4b-8a7a-e389b58fbe17.png?resizew=121)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94dd82d1afae354ad795138fb5b6919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d061c1ea5188a28fbaa19af1e19fa567.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94dd82d1afae354ad795138fb5b6919.png)
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