1 . 在四面体
中,
,
,
,点P是棱
上的动点,点Q为棱
的中点,记直线
与直线
所成的夹角为
,直线
与平面
所成的角为
,二面角
的平面角为
,则有( )
![](https://img.xkw.com/dksih/QBM/2020/7/30/2516891955380224/2518007260856320/STEM/2ce50d20-5aab-4cf9-b81a-d496584dcb3d.png?resizew=157)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1c13e2642c7d31216e7aea0980a367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://img.xkw.com/dksih/QBM/2020/7/30/2516891955380224/2518007260856320/STEM/2ce50d20-5aab-4cf9-b81a-d496584dcb3d.png?resizew=157)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
2 . 设
、
是两个不同的平面,m、n是两条不同的直线,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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7卷引用:浙江省湖州市菱湖中学2018-2019学年高三上学期期中数学试题
3 . 已知四棱锥
的底面是正方形,侧棱长均相等,E是线段
上的点(不含端点),设直线
与
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://img.xkw.com/dksih/QBM/2020/2/6/2393072097476608/2395526058770432/STEM/a5220f00828d4186af8bef483f86db76.png?resizew=251)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f91414bbba4600fce6f12441b670d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
![](https://img.xkw.com/dksih/QBM/2020/2/6/2393072097476608/2395526058770432/STEM/a5220f00828d4186af8bef483f86db76.png?resizew=251)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 在三棱锥
中,
为正三角形,设二面角
,
,
的平面角的大小分别为
,则下面结论正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fe637f1537666932491637f9b3d3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a5d8831a9bef0f3d882d97d28e6d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d75ebe3bdbb8cd4b42e37403b636a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f06157f5f65108d71d987d79dbb2a3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 如图,在
二面角的棱上有两点A、B,线段AC、BD分别在这个二面角的两个面内,并且都垂直于棱AB,若
,则线段CD的长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/4558b691-5c8b-4539-8882-e27d5e25a17d.png?resizew=204)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d97682083decd8f58dc5bd42aab2f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/4558b691-5c8b-4539-8882-e27d5e25a17d.png?resizew=204)
A.![]() | B.16 | C.8 | D.![]() |
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浙江省湖州市吴兴高级中学2021-2022学年高二上学期10月阶段性测试数学试题吉林省长春市榆树市2019-2020学年高二上学期期末数学(理)试题(已下线)人教B版2019选择性必修第一册综合测试(基础过关)-2020-2021学年高二数学单元测试定心卷(人教B版2019选择性必修第一册)重庆市第三十七中学校2020-2021学年高二上学期期中数学试题(已下线)专题03 空间向量与立体几何的压轴题(一)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)(已下线)第一章 (综合培优)空间向量与立体几何 B卷-【双基双测】2021-2022学年高二数学同步单元AB卷(人教A版2019选择性必修第一册)湖北省武汉市育才高级中学2021-2022学年高二上学期第一次月考数学试题安徽省芜湖市2021-2022学年高二上学期期中联考数学试题湖北省重点中学四校(襄阳五中、钟祥一中、夷陵中学、随州一中)2021-2022学年高二上学期联考学试题广东省佛山市南海区南海中学2022-2023学年高二上学期第一次段考数学试题湖南省郴州市嘉禾县第六中学2022-2023学年高二上学期第二次月考数学试题辽宁省大连市第八中学2021-2022学年高二上学期10月阶段考试数学试题湖北省武汉市第十九中学2023-2024学年高二上学期10月月考数学试题重庆市万州沙河中学2023-2024学年高二上学期10月月考数学试题
6 . 如图,已知三棱锥
中,平面
平面
,记二面角
的平面角为
,直线
与平面
所成角为
,直线
与平面
所成角为
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/bf2d1565-4352-4dfd-a9a7-acfeea57a638.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905e950cc8fc6f92f31c62c784cbbc26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/bf2d1565-4352-4dfd-a9a7-acfeea57a638.png?resizew=160)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 如图,已知点
是正方形
的边
上一动点(端点除外),现将
沿
所在直线翻折成
,并连接
,记二面角
的大小为
,则
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480277820293120/2480335827787776/STEM/dbd26b1b883b4e2fb1ec4c314c10dfe5.png?resizew=296)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438bf2134641f9950932bd667188d63c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17575293fcce560441d44c82aeee7574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8267d832508d4bee00ff2d4a4bd2b6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0935b808b6941672b741b5fa6ac2e85d.png)
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480277820293120/2480335827787776/STEM/dbd26b1b883b4e2fb1ec4c314c10dfe5.png?resizew=296)
A.存在![]() ![]() ![]() | B.存在![]() ![]() ![]() |
C.存在![]() ![]() ![]() | D.存在![]() ![]() ![]() |
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8 . 如图,已知三棱锥
满足
,
在底面的投影
为
的外心,分别记直线
与平面
,
,
所成的角为
,
,
,则( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/493d7547-be52-48f3-b425-36e81397ae99.png?resizew=204)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad027e4a17389a50a9da8797084c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/493d7547-be52-48f3-b425-36e81397ae99.png?resizew=204)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 如图,三棱锥
的三条棱
、
、
两两垂直,
是
的中点,
,
是
上的点,
.记二面角
,
,
的平面角分别为
,
,
,则以下结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/54a7011e-6f6c-44e7-b94f-b162c8615729.png?resizew=270)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec52dd76c0802829457ae79c6e2a42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafe92c0386debc9bb3027bd07f8cd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e209719e0601448698cb0c673795156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9ed960d92cd08e368ed56651fe6632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/54a7011e-6f6c-44e7-b94f-b162c8615729.png?resizew=270)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
10 . 如图,矩形
中心为
,现将
沿着对角线
翻折成
,记
,二面角
的平面角为
,直线
和
所成角为
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/cd5bfb67-b47b-477e-9a8d-b3c4fdc339dd.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68101f8ffeb967bc23490e566636c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f63756fe9251e65cc14e1ce9723d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a313fa9db2c50907e7341b07cdde8021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2494168ffc550b1417f20e47c13aa81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001a1ffb477e4fde288a68618803b0e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/cd5bfb67-b47b-477e-9a8d-b3c4fdc339dd.png?resizew=162)
A.![]() | B.![]() |
C.![]() | D.![]() |
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