解题方法
1 . 已知空间直角坐标系中的四个点
分别为线段
上的动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81033af8f3c067edb20337e0f55c6008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
A.三棱锥![]() ![]() | B.三棱锥![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2 . 如图,这是缠线用的线拐子,在结构简图中,线段AB与线段CD所在直线异面垂直,E,F分别为AB,CD的中点,且
,
.使用线拐子时使丝线从点A出发,依次经过D,B,C,又回到点A.这样一直循环,丝线缠好后从线拐子上脱下,这称为“束丝”.若图中
,则丝线缠一圈的长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab00e0cff0876c4183a47f1272cf9928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6cc3789c0e9b7d1226aa0de3327599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131b630c661eff546537a530140f3434.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:贵州省遵义市2023-2024学年高二下学期6月月考数学试题
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解题方法
3 . 如图,已知
平面ACD,
平面ACD,三角形ACD是正三角形,且
,F是CD的中点.
平面CDE;
(2)求直线EF与平面CBE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb59a3752da728cfa77557dd14d0f737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06781fd124cad40fa5fd120b074157f.png)
(2)求直线EF与平面CBE所成角的正弦值.
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4卷引用:河南省济源市第四中学2023-2024学年高二上学期12月考数学试卷
河南省济源市第四中学2023-2024学年高二上学期12月考数学试卷河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题(已下线)第1套 全真模拟卷 (基础)【高一期末复习全真模拟】(已下线)专题08 立体几何大题常考题型归类-期末考点大串讲(人教B版2019必修第四册)
4 . 一个圆台的上、下底面的半径分别为1和4,体积为
,则它的母线长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843cb982bb9f03500f1e300af3492c5f.png)
A.![]() | B.![]() | C.![]() | D.5 |
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2卷引用:河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
5 . 正方体
中,
,
分别在
上,且
,
,则下列正确的有( )个
①
,②
,③
,④点
到平面
距离为1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564a9f661332d97d09e82dfd6f499d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0963c102bfc6da34a4e8c4e16d503065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac240e81e4dbf3097c843b75235ec661.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e89457e4eafe86d2c6f404f967c753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661df691bacf67f20557fef29c1af1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6469878a955cc09fac22ba5aea3fb962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028856d5101687dd8eaf130846489cfd.png)
A.1 | B.2 | C.3 | D.4 |
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6 . 如图,在四棱锥
中,底面
是菱形,
为锐角,
是正三角形,平面
底面
,
,且四棱锥
的体积为2.
.
(2)若
是PC的中点,求平面
与平面
夹角的余弦值.
![](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/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
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2卷引用:贵州省遵义市2023-2024学年高二下学期6月月考数学试题
7 . 若
,
是两条不同的直线,
是一个平面,
,则“
”是“
”的( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e380108ba2cf04e68a5a9393d2b921c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dedfa42c16dd0aefa2928a6e41f3dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a4c549e7ea8776ec821c467bc1a913.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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名校
解题方法
8 . 已知梯形
,
,
,
,
,
是线段
的中点.将
沿着
所在的直线翻折成四面体
,翻折的过程中下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() ![]() |
B.当直线![]() ![]() ![]() ![]() |
C.四面体![]() ![]() |
D.四面体![]() ![]() |
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解题方法
9 . 如下图:在四棱锥
中,四边形
是边长为2的菱形,
是边长为2的等边三角形,
.
平面
;
(2)求平面
和平面
所成二面角的正弦值.
![](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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6138a2f29da66b5a2038f6f6fe9f0804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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解题方法
10 . 如下图:已知四棱台
的上、下底面分别是边长为
和
的正方形,
,且
底面
,点
满足
,点
是棱
上的一个点(包括端点),若二面角
的余弦值为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fea37dbf4145c3b311bcec0fc25ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcbc583a919eb6fecafb5a0d31ab103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a24acb11fac4bcf6a86e3e9223a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1de7da3ab92e70f135ea628a691167.png)
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