真题
1 . 如图,在直三棱柱
中,平面
侧面A1ABB1.
(Ⅰ)求证:
;
(Ⅱ)若直线AC与平面A1BC所成的角为θ,二面角A1-BC-A的大小为φ,试判断θ与φ的大小关系,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
(Ⅱ)若直线AC与平面A1BC所成的角为θ,二面角A1-BC-A的大小为φ,试判断θ与φ的大小关系,并予以证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/b28f4071-53aa-4014-995c-ca4e7f2d90af.png?resizew=151)
您最近一年使用:0次
2016-11-30更新
|
1711次组卷
|
6卷引用:2019届陕西省西安交大附中高三下学期第二次模拟考试数学(理)试题
2019届陕西省西安交大附中高三下学期第二次模拟考试数学(理)试题2008年普通高等学校招生全国统一考试理科数学(湖北卷)(已下线)2012届丹东市四校协作体高三摸底测试数学(零诊) (理)(已下线)2011-2012学年河北省正定中学高二第一学期期末考试文科数学试卷广东省广州市2023届高三上学期8月阶段测试数学试题2008 年普通高等学校招生考试数学(理)试题(湖北卷)
名校
2 . 如图,在四棱锥
中,底面
是平行四边形,
,
,
,
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9e5f1cfea3643c30c21732073a11ef.png)
(2)若平面
平面
,且
,求二面角
的平面角的余弦值.
![](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/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9e5f1cfea3643c30c21732073a11ef.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b2c408bc9b3b125c6a4219d22e4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e867e5c7ef4da37d8985ce82022060e.png)
您最近一年使用:0次
解题方法
3 . 如图,在四棱锥
中,已知底面
为矩形,侧面
是正三角形,侧面
底面
,
是棱
的中点,
.
平面
;
(2)若
,求二面角
;
(3)若二面角
为
,求异面直线
与
所成角的正切值.
![](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/852aabd89edffc1b94344ff3f1f31ccd.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
(3)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8e0c5bcf2d86726cd9f561b8ff5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
名校
4 . 如下图,四棱锥
的体积为
,底面
为等腰梯形,
,
,
,
,
,
是垂足,平面
平面
.
;
(2)若
,
分别为
,
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279e119eed905cf15026649a1b86502a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a398397362a18da1cc9f24bf3f356ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f29c3e772e56008790298824122792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7713c13736076f1fe2c139bb4a4b6d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/9104a1941e557a85fd1496bc2b9be297.png)
(2)若
![](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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ab98efd2b5fcbfeae61fe37f921a0e.png)
您最近一年使用:0次
5 . 如图1,已知正方形
的中心为
,边长为
分别为
的中点,从中截去小正方形
,将梯形
沿
折起,使平面
平面
,得到图2.
平面
;
(2)求二面角
的平面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd47f92c374cfcf7010ea0d421210580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630754333e7043c573d0ecdb64cf1246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dcd0afaef9dc32697c8bc480b1fd1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc61a86aa346c6c4b37cf60c0ea07d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40cbcf7b3bc282c656e1f266a12ee32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c9b06cf3913c7e81a8ea88a8836714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7e1bac4fc939a3af4dd3601617798d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb86687f6014ddc386829090a3e7ae4.png)
您最近一年使用:0次
2024-04-03更新
|
345次组卷
|
5卷引用:陕西省西安市高新第一中学2023-2024学年高一下学期第二次月考数学试题
陕西省西安市高新第一中学2023-2024学年高一下学期第二次月考数学试题河南省青桐鸣联考2023-2024学年高二下学期3月月考数学试题河南省青桐鸣联考2023-2024学年高二下学期3月月考数学试题(北师大版)(已下线)专题20 平面与平面的位置关系-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)专题13.5空间平面与平面的位置关系-重难点突破及混淆易错规避(苏教版2019必修第二册)
6 . 如图,在三棱柱
中,
平面
,
,
分别为
,
的中点,
为
上的点,且
.
(1)求证:平面
平面
;
(2)若三棱柱所有棱长都为
,求二面角
的平面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6efa4395e52292ef2032b0b912133b0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/10/5278ba0a-1ceb-4d5b-a89b-c8b8114323f6.png?resizew=148)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d45aac1963ee8eb5e2723893f86007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若三棱柱所有棱长都为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9489e5f82b60248c1adfcf299032b.png)
您最近一年使用:0次
名校
7 .
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)
您最近一年使用:0次
2023·江苏南通·模拟预测
名校
解题方法
8 . 如图,在多面体
中,
,
平面
,
是边长为2的正三角形,
,点M是BC的中点,
平面
.
(1)求证:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0082d25fc347d093ca69e6e0992f6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f21e690c639f6e9147c037c0d96bee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/5d477a9f-2d41-4814-b70c-d3e2d908f6ed.png?resizew=132)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3065be25fc3f94fb8af53de753fce4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e95aa49b56164ade34d8291a166ebb1.png)
您最近一年使用:0次
名校
解题方法
9 . 如图所示,在四棱锥
中,四边形
为梯形,
,
,平面
平面
.
的中点为
,求证:
平面
;
(2)求二面角
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/ff4dad92e16cd1d30393bbbcff1a5c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228e321561e1626ff83596f593e29aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa6d64d90b17044cb17ff3061420c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
您最近一年使用:0次
2023-11-16更新
|
499次组卷
|
7卷引用:陕西省西安市西安中学2024届高三上学期期末数学(理)试题
陕西省西安市西安中学2024届高三上学期期末数学(理)试题浙江省“衢温5+1”联盟2023-2024学年高二上学期期中考试数学试题(已下线)专题09 立体几何(5大易错点分析+解题模板+举一反三+易错题通关)-2(已下线)第10讲 空间的垂直关系-【寒假预科讲义】(人教A版2019必修第二册)(已下线)第二章 立体几何中的计算 专题一 空间角 微点8 二面角大小的计算综合训练【基础版】(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)(已下线)专题13.7空间中的距离和夹角问题-重难点突破及混淆易错规避(苏教版2019必修第二册)
名校
10 . 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)
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2023-06-30更新
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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