1 . 如图,在正方体
中,
为
与
的交点.
(1)求证:平面
平面
;
(2)设
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/184a55f2-3d47-4e45-94d2-fcd634e88120.png?resizew=154)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd190b5a26dfb45a06c1d6ee86dd82d9.png)
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解题方法
2 . 如图所示,在棱长为
的正方体
中,
、
分别为棱
、
的中点.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/18/f5a5a909-812d-4b5b-bc84-831bcaa6f7d9.png?resizew=169)
A.直线![]() ![]() |
B.直线![]() ![]() ![]() |
C.平面![]() ![]() ![]() |
D.平面![]() ![]() |
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3 .
是正三角形,线段
和
都垂直于平面
.设
,
,且F为
的中点,如图.
(1)求证:
平面
;
(2)求证:
;
(3)求平面
与平面
所成锐二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3b1722b100297f2fa8fad62423149d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede69346d90f2c2c7d738d90c6aa60a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/aa72c9c8-00af-4424-93b5-63c8171293c4.png?resizew=136)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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4 . 如图,在四棱锥
中,
,
,
,
,
.
时,求直线
与平面
所成角的大小;
(2)当二面角
为
时,求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6370d6c626bdabf1fc694501ee6c714f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1387a262fa090afe51656734c3422bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7ff7cf4d7094bc927e959157ef1b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a351d71fa01d3f5920e374a8ee7b524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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2023-06-30更新
|
1230次组卷
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8卷引用:陕西省西安市铁一中学国际部2023-2024学年高一下学期第三月考数学试题
陕西省西安市铁一中学国际部2023-2024学年高一下学期第三月考数学试题江苏省苏州市2022-2023学年高一下学期期末学业质量阳光指标调研数学试题(已下线)模块二 专题5《立体几何初步》单元检测篇 A基础卷 (苏教版)(已下线)第五篇 向量与几何 专题17 三正弦定理、三余弦定理 微点1 三正弦定理、三余弦定理上海市杨浦高级中学2023-2024学年高三上学期11月期中考试数学试卷四川省内江市第二中学2023-2024学年高二上学期12月月考数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点11 三正弦定理与三余弦定理(一)【培优版】(已下线)专题3 由二面角求线段长问题(解答题一题多解)
名校
5 . 如图,在四棱锥
中,
,
,
,△MAD为等边三角形,平面
平面ABCD,点N在棱MD上,直线
平面ACN.
.
(2)设二面角
的平面角为
,直线CN与平面ABCD所成的角为
,若
的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e05d8681a679bd31922e62480f69d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451604e8cbe0706585d9cd2c76db4b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74c46a80f7540470b5e171e2e17d3bf.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698335f4880c7a298f4898c83b6562bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de9d1a07d32cae0e86d73482477da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2023-06-30更新
|
2974次组卷
|
8卷引用:陕西省西安市莲湖区2022-2023学年高一下学期期末数学试题
名校
6 . 如图所示,已知三棱台
中,
,
,
,
,
.
(1)求二面角
的余弦值;
(2)设
分别是棱
的中点,若
平面
,求棱台
的体积.
参考公式:台体的体积公式为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8889bb4fe2736bdc96cc1737ed853a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc511e0c2c555bfd2532b5d3ecc12b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23ad89291eaa30b42a256f8e2b875fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89eac4972d99833acf112d298c6c508b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/cf0cfb4e-557d-4361-9918-f700c9cd215f.png?resizew=174)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9a94dd71e367f82a9e45b481dc1bfc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227c1d105f7abf228e7a4f3097ae93f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9336f9116d35f8febba112381e085da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
参考公式:台体的体积公式为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811a97b241e481d25c495996bb0779fc.png)
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7 . 截角四面体是一种半正八面体,可由四面体经过适当的截角,即截去四面体的四个顶点所产生的多面体.如图所示,将棱长为
的正四面体沿棱的三等分点作平行于底面的截面,得到所有棱长均为a的截角四面体,现给出下列四个命题:①二面角
的余弦值为
;②该截角四面体的体积为
;③该截角四面体的外接球表面积为
④该截角四面体的表面积为
,则其中正确命题的个数为( )
![](https://img.xkw.com/dksih/QBM/2023/6/19/3262925183123456/3263886087036928/STEM/881a892ad4aa4e508b04d2a6c3522da8.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4c533eae48d59a256cc7d210c23242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198a843a1cb2bf15d2f32076d3826e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aecf3ee6a59c3fae5285c15de9102f1.png)
![](https://img.xkw.com/dksih/QBM/2023/6/19/3262925183123456/3263886087036928/STEM/881a892ad4aa4e508b04d2a6c3522da8.png?resizew=165)
A.![]() | B.![]() | C.![]() | D.![]() |
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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)
您最近一年使用:0次
2023-11-10更新
|
238次组卷
|
2卷引用:陕西省西安市南开高级中学2023-2024学年高二上学期12月月考数学试题
名校
9 . 已知正三棱柱
中,
,D为AC边的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf0b9bd7a2d1dd5afefbed5fd395d3e.png)
(1)求侧棱长;
(2)求三棱锥D-
的体积;
(3)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf0b9bd7a2d1dd5afefbed5fd395d3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/18/da233420-539d-4588-954b-618e88ac7969.png?resizew=185)
(1)求侧棱长;
(2)求三棱锥D-
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f664c0db517bec6886ff0b6100fd474.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ceb31247add8ca7b0853e801e1d125.png)
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10 . 在三棱锥
中,△ABD和△CBD均为边长为2的等边三角形,且二面角
的平面角为
,则三棱锥的外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-06-13更新
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287次组卷
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3卷引用:陕西省西北工业大学附属中学2022-2023学年高一下学期第二次月考数学试题
陕西省西北工业大学附属中学2022-2023学年高一下学期第二次月考数学试题江西省乐安县第二中学2022-2023学年高一下学期6月期末数学试题(已下线)专题突破:立体几何外接球的常见模型-同步题型分类归纳讲与练(人教A版2019必修第二册)