名校
1 . 如图,在四棱锥
中,底面
是等腰梯形,
,侧面
平面
,
,
,
为
的中点.
(1)证明:
平面
;
(2)点
在棱
上,直线
与平面
所成的角的正弦值为
,求
的值.
![](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/34e0a957a55460c72673c0f2ee90dbb3.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/b70e550fa3c5aaf1b9c28f36fd5ed5d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77c16357eabed95d85bbd4e3dada92e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/f371ba93-80ea-4449-aaea-b02b100c3d14.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44cd09d9ad46264de4620c60370d49d.png)
(2)点
![](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/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44cd09d9ad46264de4620c60370d49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241a37fb1eff68a7133822b1b52d627e.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,
是边长为3的正方形,
平面
,
,
,
与平面
所成角为60°.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/c5720013-3548-4f6e-a718-7b6e9d250117.png?resizew=101)
(1)求证:面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8781208b8fe41342b9bd8b20456cdba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5624c7941eb3cca11d8efbe76d9af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/c5720013-3548-4f6e-a718-7b6e9d250117.png?resizew=101)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f717b7d4d0978eec7330afec554c078.png)
您最近一年使用:0次
3 . 四棱锥
中,
平面
,
,
,
,
.
(1)求证:
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ead1fc354cc5dac0bfd288e6d0dd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be41b05e11ba5eadaaed9a224b949774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/10c818ab-5e69-4dd7-a815-5e4e93d284cc.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c7a937699f989b685f285041434000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
您最近一年使用:0次
名校
解题方法
4 . 已知四棱柱ABCD﹣A1B1C1D1的底面是边长为2的菱形,且∠BAD=
,AA1⊥平面ABCD,
,设E为CD的中点.
(1)求证:D1E⊥平面BEC1;
(2)点
在线段A1B1上,且AF∥平面BEC1,求平面ADF和平面BEC1所成锐角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bbaa1516ed924a27d7b5cbf81ebba4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/e0bf0eff-bfdb-4f74-ac99-c71cb194a1d5.png?resizew=164)
(1)求证:D1E⊥平面BEC1;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
2024·全国·模拟预测
名校
5 . 如图,P为圆锥的顶点,O为圆锥底面的圆心,AB为底面直径,四边形POBC是梯形,且
,
,
,D为圆O上一点.
(1)若点M在线段AD上,且
,求证:
∥平面CDB;
(2)当直线PD与平面PAB所成的角为30°时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061248f4e3932ad43c1abd52ada56a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b93b8e3f2196f571782a283f2e10ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3530ee12bd68b53970b83f28985b31.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/b1f43728-6dfd-4cfb-9393-8828e4fb8ffa.png?resizew=168)
(1)若点M在线段AD上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963f0cda34e54f15725cee9448a4537e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
(2)当直线PD与平面PAB所成的角为30°时,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6a0cee8226e82cc57916e10d533369.png)
您最近一年使用:0次
2024·全国·模拟预测
名校
解题方法
6 . 如图1,已知四边形
为直角梯形,
,
,
,M为CF的中点.将
沿
折起,使得点C与点A重合,如图2,且平面
平面
,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/740bf62c-3246-44e8-aa97-670e503b7bd6.png?resizew=340)
(1)求证:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4b2821a057ba455da22886232e0188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9e5ad901b5ac2d256c6f0a141a1554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c2823355f9c78fadd25833f400d710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e59b7c0d4a0b312e674b7bb061240b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb5012f6c70a1e98d682b6d021fadd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fb56bc46444a0d05164098be46717d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0261cc5d9ab883cbf7691faf3acbee67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6630f6d35f97c30b95d803f43c5aac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/740bf62c-3246-44e8-aa97-670e503b7bd6.png?resizew=340)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe3abee84ca1c3fa8fa6503786f497e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868a98a5d6337c3dd9bca228e3545665.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eef2a1ef0b40bbce38544c57408e82b.png)
您最近一年使用:0次
名校
7 . 如图,在四棱锥P﹣ABCD中,
⊥底面
,
,
,
,点E为棱
的中点.
(1)证明:
;
(2)求直线
与平面
所成角的正弦值;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860850e8013f9399382f9344112725cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/387f9745-e10a-46be-b422-74d0b62b660e.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c38bbe49284a2ceab26001ced8cfd56.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba0dd982b283611f4d01be499546af9.png)
您最近一年使用:0次
2024-01-05更新
|
480次组卷
|
3卷引用:宁夏石嘴山市第三中学2016-2017学年高二上学期期末数学(理)试题
名校
解题方法
8 . 如图,在四棱锥中,平面
底面
,
,在AD边上取一点E,使得
为矩形,
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6901b65890d2acb77a437d386c565f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db610620932bac7491424635583579b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9428c4a6a25d360a036aaf0a92e40988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在三棱柱
中,
,
,D,E分别是CB,CA的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/b13d9e2d-c34b-4c78-83db-681c10945d10.jpg?resizew=164)
(1)若平面
平面
,求点
到平面ABC的距离;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9332278351ab92e03e984e9279dd06a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45224f7eac9d0cef64bf28d93e7721a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fec64454070a31334375468ad17d2eb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/b13d9e2d-c34b-4c78-83db-681c10945d10.jpg?resizew=164)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1225db7039505351a11f64841ec0af2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2023-12-20更新
|
275次组卷
|
5卷引用:宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(五)
10 . 如图,在四棱锥
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/4b937e57-9ebd-4b89-ae02-824272e1ecc9.png?resizew=175)
(1)求证:平面
平面
;
(2)若
,点
是
中点,且四棱锥
的体积为
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2d5ab801f2a84b78139b0ea2c5032b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b2f446cccf2652c090e99a75beb3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/4b937e57-9ebd-4b89-ae02-824272e1ecc9.png?resizew=175)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.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/9e5ba482836565abad208665cf7b9972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac93e58e9bba899df62a4cda5f1a5ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2023-11-28更新
|
222次组卷
|
2卷引用:宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(四)