1 . 如图1,在直角梯形中,
,
,
,
是
的中点,
与
交于
点,将
沿
向上折起,得到图2的四棱锥
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cb953004dcb6e4dd6880e8be5202c6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db51de0d0a68d4c12787cf3ee1609205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17ae0eaea601d6b62be05cfce86c5ca.png)
您最近一年使用:0次
2 . 如图,在平行四边形
中,
,
,
,将
沿
折起到
,满足
.
平面
;
(2)若在线段
上存在点
,使得二面角
的大小为
,求此时
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea25ef38e4afa8f75ffd0842890289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1ba548d839b5d5cf74bdd6884cd97c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe052786101dfcc941480919eb2cecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64785e4401e1d79632e360fd3626ed62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在长方体
中,点
在平面
的射影为
.
(1)证明:
为
的垂心.
(2)若
,且点
在平面
的射影为点
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/37e61b98-1318-418f-b939-6e590a30b023.png?resizew=217)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de60f6ffd5ab327d4cfe32d26d95da70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ab5a353686725ea697ea410a8ad9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577b7032795d3900dbce9cbe60ab2a1d.png)
您最近一年使用:0次
2023-07-05更新
|
541次组卷
|
4卷引用:河北省保定市定州市2022-2023学年高一下学期期末数学试题
名校
4 . 如图,在四棱锥P-ABCD中,平面PDC⊥平面ABCD,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,
,E为PD中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/96c6fbf0-2f3b-4afa-b65a-627e1ae5b294.png?resizew=155)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
面PAB;
(2)点Q在棱PA上,设
,若二面角P-CD-Q余弦值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ae3a518db7bc947a604fb567337f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1117057d2a8b2681965b937e1b5f4749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6037bba27008abc96a6dba99753549ad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/96c6fbf0-2f3b-4afa-b65a-627e1ae5b294.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)点Q在棱PA上,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ab692e3febad6702110040324c597d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ec70bc9d4f8f5df312e2f09ee3bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-04-24更新
|
1859次组卷
|
4卷引用:河北省保定市部分高中2024届高三上学期期末数学试题
22-23高一·全国·课后作业
名校
5 . 如图,四棱锥
中,
平面
,
,
.过点
作直线
的平行线交
于
为线段
上一点.
平面
;
(2)求平面
与平面
所成二面角的余弦值.
![](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/f15cafcf9c9871250c02e036e0ddb9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc50a2a5541f356f1ce9813ebb86cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09219dbd440c70d66bf2bf8b4c2bfe2f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
您最近一年使用:0次
2023-03-12更新
|
2377次组卷
|
11卷引用:河北省石家庄市辛集市2022-2023学年高一下学期期末数学试题
河北省石家庄市辛集市2022-2023学年高一下学期期末数学试题(已下线)8.6.2 空间角与空间距离(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)第18讲 基本图形位置关系(已下线)第八章:立体几何初步 章末检测试卷(已下线)8.6.3 平面与平面垂直(1)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)13.2.4 平面与平面的位置关系 (2)(已下线)专题强化二:异面角、线面角、二面角的常见解法 (1)广东省东莞市东莞中学松山湖学校2022-2023学年高一下学期第二次检测数学试题江西省宜春市丰城拖船中学2023届高三一模理科数学试题专题12空间中直线、平面的平行与垂直关系(解答题)(已下线)湖南省长沙市雅礼中学2023-2024学年高一下学期期中考试数学试题变式题16-19
6 . 如图,直三棱柱
的体积为4,点
,
分别为
,
的中点,
的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/3/0c0b6a12-5e43-4fb2-b93b-8f6e9ed2096a.png?resizew=144)
(1)求点A到平面
的距离;
(2)
,平面
平面
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c941cb13f64020851fd09e0514f2502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/3/0c0b6a12-5e43-4fb2-b93b-8f6e9ed2096a.png?resizew=144)
(1)求点A到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14172212b7b34eaf967c5a72233621c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152cfd5011c94e02c1a9cbbd4d8f58bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
您最近一年使用:0次
2023-01-18更新
|
855次组卷
|
5卷引用:河北省定州市2022-2023学年高二上学期期末数学试题
河北省定州市2022-2023学年高二上学期期末数学试题(已下线)模块四 专题5 暑期结束综合检测5(能力卷)(人教B)湖北省襄阳市宜城市第一中学2023-2024学年高二上学期9月月考数学试题(已下线)高二上学期第一次月考解答题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)湖北省宜昌市枝江市第一高级中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
7 . 如图,在多面体
中,底面
为正方形,
平面
,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/85173386-fd46-4e45-b0fb-07ed636f8b29.png?resizew=171)
(1)求证:
平面
;
(2)若
,求
与平面
所成角的正弦值;
(3)若
平面
,求平面
与平面
夹角的余弦值.
![](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/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8015cb25a477e921afee820e747c2989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/85173386-fd46-4e45-b0fb-07ed636f8b29.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc521258fcaeaf7acffc5ae98c3af6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4280be91682e5d8a0d0704190319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
您最近一年使用:0次
2023-01-06更新
|
647次组卷
|
3卷引用:河北省邯郸市魏县2022-2023学年高二上学期期末考试数学试题
河北省邯郸市魏县2022-2023学年高二上学期期末考试数学试题天津市第九中学2022-2023学年高三上学期期末数学试题(已下线)河北省石家庄市河北省实验中学2024届高三上学期名校联考数学试题变式题19-22
名校
解题方法
8 . 异面直线、
上分别有两点A、B.则将线段AB的最小值称为直线
与直线
之间的距离.如图,已知三棱锥
中,
平面PBC,
,点D为线段AC中点,
.点E、F分别位于线段AB、PC上(不含端点),连接线段EF.
(1)设点M为线段EF中点,线段EF所在直线与线段AC所在直线之间距离为d,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115cd1e6611743bc19995a010e3a09dd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eace15563ef7f4f77ddf029e89ac5152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3a9239e2774185f03738d0dc467e32.png)
您最近一年使用:0次
2023-01-03更新
|
2403次组卷
|
7卷引用:河北省邯郸市魏县第五中学2022-2023学年高二上学期期末数学试题
河北省邯郸市魏县第五中学2022-2023学年高二上学期期末数学试题河北衡水中学2023届高三模拟数学试题(已下线)模块十一 立体几何-2(已下线)专题1 利用空间向量求距离(2)(已下线)专题02 空间向量研究距离、夹角问题(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)(已下线)第二章 立体几何中的计算 专题二 空间距离 微点10 空间两条直线的距离(六)【培优版】(已下线)3.4.2 求距离(六大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
9 . 如图,在三棱柱
中,底面是边长为2的等边三角形,
分别是线段
的中点,二面角
为直二面角.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/cd2ffec7-455a-44dc-b840-b1e30658bad4.png?resizew=217)
(1)求证:
平面
;
(2)若点
为线段
上的动点(不包括端点),求锐二面角
的余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5056fb4a4e47b4f2bb80b35df5abad48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d06f8edd1a1f18ca2dae700c6a29ab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfeb93372b5ff8acf1f88d82a6086218.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/cd2ffec7-455a-44dc-b840-b1e30658bad4.png?resizew=217)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e5777a34d4761364c48e2b53ab79ff1.png)
您最近一年使用:0次
2022-11-22更新
|
1726次组卷
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10卷引用:河北省石家庄市辛集市2022-2023学年高二下学期期末数学试题
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解题方法
10 . 如图,已知直三棱柱
,
,
,
,点
为
的中点.
平面
;
(2)求直线
与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c920d02068d0e63ffdab70786c526d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
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