名校
解题方法
1 . 如图,四棱锥
的侧面
是边长为2的正三角形,底面
为矩形,且平面
平面
,M,N分别为
的中点,直线PC与面
所成角的正切值为
.
平面
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/8825bcbd548f4eea8c8c221acdff7aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014c4c0d6c8e50e5c6c83e857f9ecac7.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,半圆的半径为2,点
四等分半圆,点
分别是
上的点,将此半圆以
为母线卷成一个圆锥,使得
,且平面
平面
.
;
(2)若平面
平面
,证明:
;
(3)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d1fdf1d417bf19e377e44d279014d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c031952601f5e4f1837f2c281720fbec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab003bd4e9f03fba43e8080fe6b78637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3066befa5750964166ddc008f247b13.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eba5fdef34d2cf7a0154a40da87128b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902d22410708695a5822daa3c672494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7218869e4014b0f5bba8822e5f8a16.png)
(3)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e2f55dceec60d80332d4f787372d2b.png)
您最近一年使用:0次
3 . 如图,以正方形
的边
所在直线为旋转轴,其余三边旋转120°形成的面围成一个几何体
.设
是
上的一点,
,
分别为线段
,
的中点.
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cfa6b4db3a67fcd3c169fd8502a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4193fb98c610f41f9a6c89d046f13d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fb768fc63e1aabddbfb2b3e7c5b51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4d775e9fb8bca58a25e75d5b21b05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57043f1d131e9c7c8b71bf8a68bacbc.png)
您最近一年使用:0次
4 . 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
|
3640次组卷
|
7卷引用: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
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
5 . 如图,在四棱柱
中,底面
为直角梯形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c64554738afc02efb17f44d8327435f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
平面
;
(2)若
平面
,求二面角
的正弦值.
![](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/5c64554738afc02efb17f44d8327435f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48dd45792ea86f80636e7eefc4040401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2095691cd6e3e50722061cbc0bb648.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f9dc20130f5eb095a2c9ab15d320b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c466a29d7af75cc71663c502d87c260.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,底面
为矩形,侧面
底面
,侧棱
和侧棱
与底面
所成的角均为
,
,
为
中点,
为侧棱
上一点,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/2b4b68ee-7d40-407e-9ab1-a79d6224add0.png?resizew=144)
(1)请确定点
的位置;
(2)求平面
与平面
所成夹角的余弦值.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132fc900a3e6678ee9854599ad6bfd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a04ea8ebc597fd1f5d6bb8df181a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/2b4b68ee-7d40-407e-9ab1-a79d6224add0.png?resizew=144)
(1)请确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2024-02-08更新
|
662次组卷
|
3卷引用:福建省漳州市2024届高三毕业班第二次质量检测数学试题
名校
7 . 如图所示,等边
所在平面与菱形
所在平面相垂直,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b85d7d422571c4cc3aa5e09505fd67.png)
平面
;
(2)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba4d0b54a0b2104e1c3a2061e4bffc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9087c01257b50f3bb8b6490d8804dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b85d7d422571c4cc3aa5e09505fd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2023-08-16更新
|
528次组卷
|
2卷引用:福建省同安第一中学2023-2024学年高二下学期第1次月考(4月)数学试卷
名校
解题方法
8 . 如图所示,在四棱锥
中,四边形ABCD是梯形,
,
,E是PD的中点.
平面PAB;
(2)若M是线段CE上一动点,则线段AD上是否存在点
,使
平面PAB?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e306e30d3159e4a68435c3fcfc8da693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
(2)若M是线段CE上一动点,则线段AD上是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
您最近一年使用:0次
2023-09-09更新
|
796次组卷
|
5卷引用:福建省福州屏东中学2023-2024学年高一下学期期中考试数学试卷
福建省福州屏东中学2023-2024学年高一下学期期中考试数学试卷(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)(已下线)8.5.3 平面与平面平行【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)6.4 .2 平面与平面平行-同步精品课堂(北师大版2019必修第二册)浙江省嘉兴八校联盟2021-2022学年高一下学期期中联考数学试题
名校
9 . 如图,
平面
,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/7/7dab7d69-2f20-4534-a438-bd9f08d7fc78.png?resizew=164)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](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/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f555fb7ea6e77a6e0fe38586a3992d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2e1bc36d99480493977801b166720d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/7/7dab7d69-2f20-4534-a438-bd9f08d7fc78.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2023-04-06更新
|
590次组卷
|
3卷引用:福建省福州第八中学2023-2024学年高二上学期期末考试数学试卷
福建省福州第八中学2023-2024学年高二上学期期末考试数学试卷湖北省襄阳市第一中学2022-2023学年高二上学期期末数学试题(已下线)期末测试卷01(测试范围:第1-4章数列)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)