解题方法
1 . 已知:如图,
为正三角形,AE和CD都垂直于平面ABC,且
,点
是
的中点.
平面ABC;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ed9e594c8562b84cf1e0e18b272e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,直四棱柱
的底面为平行四边形,
分别为
的中点.
平面
;
(2)若底面
为矩形,
,异面直线
与
所成角的余弦值为
,求D到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814ef3feb3329aab66213f3a6a9d2f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
(2)若底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc28e69c1ba0aac981256887f7dfa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a604466a9c8d10d557b3dfc43b547065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在五面体
中,底面
为正方形,
.
;
(2)若
为
的中点,
为
的中点,
,再从条件①、条件②这两个条件中选择一个作为已知,求直线
与平面
所成角的正弦值.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答计分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410666db488a1c79eca80e51f4278e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666734423f1818d76a74f171b7420b68.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6e498f70417224e1f3cf28c5b88df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1976e2a7028cacd09bd7a83ca89bd23.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc5df62e8ac9c74a46462519b95479a.png)
注:如果选择条件①和条件②分别解答,按第一个解答计分
您最近一年使用:0次
2024-04-08更新
|
1975次组卷
|
6卷引用:模块五 专题1 全真基础模拟1(苏教版高二期中研习)
(已下线)模块五 专题1 全真基础模拟1(苏教版高二期中研习)北京市东城区2023-2024学年高三下学期综合练习(一)(一模)数学试题(已下线)模块3 第6套 全真模拟篇广东省梅县东山中学2024届高三下学期第一次模拟考试数学试题(已下线)模块三 专题3 高考新题型专练 专题1 劣构题专练(苏教版)江苏省南京航空航天大学苏州附属中学2023-2024学年高三下学期二模阳光测试数学试题
2024高二·全国·专题练习
解题方法
4 . 如图,四棱锥
中,四边形
是矩形,
,
,
为正三角形,且平面
平面
,
、
分别为
、
的中点.证明:
平面
;
![](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/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.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/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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a7c298441968300f7653f59e837fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
名校
5 . 如图,在四棱锥
中,
为
中点,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/f5aafd27-9bc9-4225-9c54-0a9892adc3aa.png?resizew=165)
(1)求证:
平面
;
(2)在棱
上是否存在点
,使得平面
与平面
夹角的余弦值为
?若存在,求出点
的位置;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ad6a0124359e8b9f7649cf0bff51ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4040c8a8df7c9af9247e15cd676b442b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/f5aafd27-9bc9-4225-9c54-0a9892adc3aa.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe67036b4671b5d2a5c55b48c4d3bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2024-01-11更新
|
1077次组卷
|
6卷引用:河南省部分高中2023-2024学年高二上学期1月联考数学试题
河南省部分高中2023-2024学年高二上学期1月联考数学试题(已下线)高二数学开学摸底考02(北师大版,范围:选择性必修第一册全部)-2023-2024学年高二数学下学期开学摸底考试卷(已下线)高二数学开学摸底考01(北师大版,范围:选择性必修第一册全部)-2023-2024学年高二数学下学期开学摸底考试卷(已下线)专题13 空间向量的应用10种常见考法归类(3)(已下线)专题05 空间向量与立体几何(解密讲义)江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(五)
2024·全国·模拟预测
名校
6 . 如图,为圆锥的顶点,
为圆锥底面的圆心,
为底面直径,四边形
是梯形,且
,
为底面圆周上一点,点
在
上.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963f0cda34e54f15725cee9448a4537e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e076c4c39e0591ed69ff780fb5a1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176b7beb3ee58b075801d6d7f6af1a4f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4dbea6a5faecdd8f6c06cf9fd43a90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6a0cee8226e82cc57916e10d533369.png)
您最近一年使用:0次
2023高二上·全国·专题练习
解题方法
7 . 如图,在四棱锥
中,
底面
,
,
,
,
,点E为棱PC的中点.证明:
![](https://img.xkw.com/dksih/QBM/2024/2/18/3435596710240256/3458978985533440/STEM/06f46867b79c41e4aca937d2de8667aa.png?resizew=161)
(1)
平面
;
(2)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51fc7d1b20a1ce1761714c1733f0511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729d5cb74bb927aa549ce596a35b26b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b175a9ea8c1c191810c1e324a5a9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9fa8832f98b5418a7d75892f7951b8.png)
![](https://img.xkw.com/dksih/QBM/2024/2/18/3435596710240256/3458978985533440/STEM/06f46867b79c41e4aca937d2de8667aa.png?resizew=161)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5258a6f9c63914b9e2ec95b6d39313b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3520ee9cc97a075e889e1625dba1157c.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65997b09d0cb2d4a7e46596c1a019e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3520ee9cc97a075e889e1625dba1157c.png)
您最近一年使用:0次
名校
解题方法
8 . 已知在四棱锥
中,底面
是矩形,且
,
,
平面
,
、
分别是线段
、
的中点.
;
(2)在线段
上是否存在点
,使得
平面
,若存在,确定点
的位置;若不存在,请说明理由.
![](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/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb2fbbce7207d2b2bdd5c5ab61ecd04.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8badfeb9e7556486e02ab60df4dd32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0901e2f5cefe6468cbbcaa332287d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2023高二上·全国·专题练习
9 . 如图,在四棱锥
中,
底面
,四边形
为正方形,
,E,F分别是AD,PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/7432ce76-83be-4749-a07d-01fe91beae69.png?resizew=158)
(1)证明:
平面
;
(2)求直线PB与直线CE所成角的余弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d4c42112e0a22f240ce2ae432e5b4d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/7432ce76-83be-4749-a07d-01fe91beae69.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求直线PB与直线CE所成角的余弦值.
您最近一年使用:0次
2023高二上·全国·专题练习
10 . 如图所示,已知多面体
中,四边形
为菱形,
为正四面体,且
.
(1)证明:
平面ABF;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fc1129846f37afdafd751627c450d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d550d73a827da587dffcb52e554affe4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/05aa2c03-490a-4276-ad1e-e7d57b4cf55d.png?resizew=192)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22eea13efafb003e7b08a6f0bc0f2f3.png)
您最近一年使用:0次