名校
1 . 如图,四棱锥
的底面是菱形,
平面
,
,点
分别是
的中点,
.
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
(3)求平面
与平面
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/2c8c336bafb3d814f6c6ba433470a6e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e1743df8bb662a1ffad47de474963b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52041559f8fee18bfa3e2e2ac07c3bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108814a3d763c02025ec48c0a68903a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0de99bbcaace58f757e5229553118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071159cac13097ea0928285bc1be66d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2fef2c0e49ecae8688ca60802310e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
您最近一年使用:0次
2 . 如图所示正四棱锥
,
,
,
为侧棱
上的点,且
,求:
的表面积;
(2)若
为
的中点,求证:
平面
;
(3)侧棱
上是否存在一点
,使得
平面
.若存在,求
的值;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f08faa7f1550cb3732de12b2be5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058695a1341735a4946257518067917a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510cad489ea9604845d41a1795b2b7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002a3b0ffc896755f903da63e3989576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bee4299dd5fffb98f9c8b5c368c3504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f08faa7f1550cb3732de12b2be5fe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15057403dfc0a732373b407f50e4137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f696e763748cf6c5437f09f317d53e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576cff1447fca473df4bf4a9245e44fb.png)
(3)侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c9ca3af3eb8bc486f7b3f29f5065eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5258a6f9c63914b9e2ec95b6d39313b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d39f37441ee55dbc8f1a6ca199a66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee29ea55624e5cbca858f47ef7ec49e.png)
您最近一年使用:0次
2024-04-15更新
|
3646次组卷
|
7卷引用:辽宁省沈阳市东北育才学校双语校区2023-2024学年高二下学期4月自主测评数学试题
辽宁省沈阳市东北育才学校双语校区2023-2024学年高二下学期4月自主测评数学试题(已下线)8.5.3 平面与平面平行【第二课】“上好三节课,做好三套题“高中数学素养晋级之路福建省晋江二中、奕聪中学、广海中学、泉港五中、马甲中学2023-2024学年高一下学期期中考试数学试题海南省海口市琼山华侨中学2023-2024学年高一下学期期中考试数学试卷广东省湛江市第二十一中学2023-2024学年高一下学期期中考试数学试卷(已下线)专题3.5空间直线、平面的平行-重难点突破及混淆易错规避(人教A版2019必修第二册)吉林省长春外国语学校2023-2024学年高一下学期5月期中考试数学试题
名校
3 . 如图,在直三棱柱
中,
分别为
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若点
是棱
上一点,且直线
与平面
所成角的正弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9566510295543eeac41ec809a3df639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4dfea6353fc25e88535e865a4982cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
您最近一年使用:0次
2024-01-19更新
|
959次组卷
|
4卷引用:北京市门头沟区大峪中学2023-2024学年高二下学期开学考试数学试题
北京市门头沟区大峪中学2023-2024学年高二下学期开学考试数学试题北京市东城区2024届高三上学期期末统一检测数学试题(已下线)广东省深圳中学2023-2024学年高三寒假开学适用性考试数学试题宁夏吴忠市2024届高三下学期高考模拟联考试卷(二)理科数学试题
名校
4 . 如图,在四棱锥
中,底面四边形
为菱形,
平面
,过
的平面交平面
于
,
.
(1)证明:
平面
;
(2)若平面
平面
,
,四棱锥
的体积为
,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/a8bc5d8308a060d6068cfc9f69fe79e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17973de4ce4eabc1013a30c588fb095e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/fd151533-3dc7-4d2a-bd8c-ca60c1b7ce0e.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf227a1e3c2f659eb66b91b85e4a947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c92660aca0ac503d9f1c75c0f77bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
5 . 如图,在四棱柱
中,底面是边长为2的菱形且
,点
在底面
上的射影为边
的中点
,点
分别为边
的中点.
平面
;
(2)若
,求直线
与平面
所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dfda77ecf61013170a6f43b4d9d116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93fa937325f9d083ac2d059cae553c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a779876cdfb2c489ad0eaed0f73e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8340db80fbc422d538f3583eaeb571.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed487430a5b8a330f2d0c52166521a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8340db80fbc422d538f3583eaeb571.png)
您最近一年使用:0次
6 . 如图,
平面
,四边形
为矩形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/f347f03e-11c6-44ce-8eee-1420d7a0cab1.png?resizew=144)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.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/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325cbcd4b35b95eac598a8403c200e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603d9d99e8cacfe71e0f83ce425cecc1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/f347f03e-11c6-44ce-8eee-1420d7a0cab1.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94270844f197d524bf1da4f1385befd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
名校
7 . 如图,在直四棱柱
中,四边形
为梯形,
,
,点
在线段
上,且
为
的中点
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516121599c9fcc528121c00afcf52fc.png)
平面
;
(2)若直线
与平面
所成角的大小为
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb00c5327825200bf9b1bde4401760b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0c2acd925d51e6960c8b427a0b5a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/f276bce4-f7f0-4920-92b1-868b33a5e2c9.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516121599c9fcc528121c00afcf52fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff3ccea5989c60e51e321af3f53f54.png)
您最近一年使用:0次
8 . 如图,在四棱锥
中,
,
,点P是以AB为直径的半圆上的一点(不同于A,B两点),平面
平面ABCD,E,F分别为线段AD,PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/24d99452-876e-4535-ad8e-fd0e9f913157.png?resizew=161)
(1)求证:
平面PAB;
(2)当四棱锥
的体积最大时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899f82187d0591696c36ff4bbf74070d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/24d99452-876e-4535-ad8e-fd0e9f913157.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)当四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b0dc4f92cba842f44477bc9811065c.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在四棱锥
中,
面
,且
,
分别为
的中点.
(1)求证:
平面
;
(2)在线段
上是否存在一点
,使得直线
与平面
所成角的正弦值是
?若存在,求出
的值,若不存任,说明理由;
(3)在平面
内是否存在点
,满足
,若不存在,请简单说明理由;若存在,请写出点
的轨迹图形形状.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcf75eebbbc06b7571c869debc3db6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c98d5943239266fd56121a5a9e241ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1457d2e76a5b86de1abf121c51eb9d35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/08d2ba78-0259-4a75-9f1e-12deec419967.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241a37fb1eff68a7133822b1b52d627e.png)
(3)在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2da5312b15f602fcb8c0ffe9ea57a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
2023-11-03更新
|
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7卷引用:专题01 空间向量与立体几何(3)
(已下线)专题01 空间向量与立体几何(3)河南省驻马店市2023-2024学年高二上学期1月期终考试数学试题(已下线)第3章 空间向量及其应用(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)辽宁省实验中学2023-2024学年高二上学期期中数学试题(已下线)专题4 大题分类练(空间向量与立体几何)拔高能力练 高二期末(已下线)第三章 空间轨迹问题 专题二 立体几何中位置关系类动点轨迹问题 微点2 立体几何中位置关系类动点轨迹问题综合训练【培优版】宁夏银川市银川一中2024届高三上学期第五次月考数学(理)试题
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10 . 如图,在四棱锥
中,
平面
为矩形,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/743255c0-9212-4e41-86ab-3908432a857e.png?resizew=136)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
.
(2)若
,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/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654c6391665a5aee872901309abd4b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044fc06badbda5c3f7882af087e8ce9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/743255c0-9212-4e41-86ab-3908432a857e.png?resizew=136)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585b9bbafa936929b1e77fe38b8ef4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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