名校
1 . 如图所示,
是边长为2的等边三角形,
平面
,
是
的中点.
(1)求证:
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f6e3552eddd977fc8560d5316769a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/23/0bc9a75e-661b-4bdc-9246-296b32504a17.png?resizew=107)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564376a88fa74090de9f7694226a6184.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
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名校
解题方法
2 . 如图,二面角
的棱上有两点
,线段
与
分别在这个二面角的两个面内,并且都垂直于棱
,若
,则二面角
的大小为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/1478cf78-d1fc-478a-ac28-9411a33ac0d8.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b8525b0f495429f6aef029642aaa64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/1478cf78-d1fc-478a-ac28-9411a33ac0d8.png?resizew=167)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-29更新
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254次组卷
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4卷引用:辽宁省大连市第二十四中学2022-2023学年高二上学期期中数学试题
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3 . 正四面体ABCD中异面直线AB与CD所成角为
,侧棱AB与底面BCD所成角为
,侧面ABC与底面BCD所成的锐二面角为
,则( )
![](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)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-07-06更新
|
718次组卷
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3卷引用:辽宁省大连市第八中学2023-2024学年高二上学期期中考试数学试题
辽宁省大连市第八中学2023-2024学年高二上学期期中考试数学试题江苏省常州高级中学2022-2023学年高一下学期期末数学试题(已下线)江苏省高一下学期期末真题必刷 -期末考点大串讲(苏教版(2019))
4 . 如图,三棱锥
中,
,
.
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de13256f52663ee5809a964eb28725bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1385c59d0fe2bc62fed70a2d13a5e956.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/f322246c-e0e0-48b4-aef3-4736c5de432f.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99116c812715c5e15ee73d088da4c253.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5768a8d6630375daf58e971fa200c5.png)
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2023-07-05更新
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2卷引用:广东省惠州市惠东县惠东荣超中学2023-2024学年高二上学期开学考试数学试题
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解题方法
5 . 一个正六棱锥,其侧面和底面的夹角大小为
,则该正六棱锥的高和底面边长之比为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 阳马,中国古代算数中的一种几何形体,是底面为长方形,两个三角面与底面垂直的四棱锥体.如图,四棱锥
就是阳马结构,
平面
,且
,连接
,
,
分别是
,
的中点.
(1)证明:
平面
;
(2)求平面
与平面
所成二面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32916a1840bdcee14580e2c5f97a92f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/2c166fbd-629f-4ce7-bd20-296c1ef2b86e.png?resizew=180)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfaad4c4467e27421876d8f2a4371d2.png)
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2023-07-04更新
|
713次组卷
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2卷引用:江西省宜春市丰城市第九中学2023-2024学年高二上学期开学考试数学试题
7 . 如图所示,平面
平面
,四边形
为矩形,
,
,
,
.
(1)求多面体
的体积;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5628323a7eeb11213df5c9048b3543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedde879f99aed69d745d5ec8fe62084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc59fd5507a10eb2fcaa6ee8a04ce21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/c8b22850-b4b5-4616-af82-1c023ccdb17a.png?resizew=139)
(1)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d65b5127ccd01345f8bca5d8a94bc4.png)
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|
1022次组卷
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3卷引用:2023年湖南省普通高中学业水平合格性考试数学试题(专家B卷)
名校
解题方法
8 . 如图,四棱锥
中,底面
为平行四边形,且
,
,
,
,则二面角
的余弦值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ad1b58fb91436d93b79df214b0ca23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5c40f909fae89547423350cd87398d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08aa6fd52f3933cbded9ce8c880b4a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65fd7291a1958bd12a0e8e1494e1d54.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/c864306f-b61c-4ff4-948a-27bb58e270b1.png?resizew=157)
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2023-11-10更新
|
238次组卷
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2卷引用:广东省东莞市东莞中学2022-2023学年高二上学期第一次段考数学试题
名校
9 . 直四棱柱
,
,AB⊥AD,AB=2,AD=3,DC=4
(1)求证:
;
(2)若四棱柱体积为36,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/12/0a295256-a2bc-4474-bd4c-50cff71f89d4.png?resizew=142)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114abfd06c4a8f7df0b0d24993206640.png)
(2)若四棱柱体积为36,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab6ad3d3e3064fa417a02dba02dbf04.png)
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2023-06-11更新
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2卷引用:上海市闵行(文琦)中学2023-2024学年高二下学期3月月考数学试题
10 . 已知二面角
的大小为
,直线
,
与
所成的角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d2a947e3fdc214d40a7d3f54679a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() |
C.当![]() ![]() ![]() ![]() | D.以上说法都不对 |
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