名校
1 . 如图,已知在圆柱
中,A,B,C是底面圆O上的三个点,且线段
为圆O的直径,
,
为圆柱上底面上的两点,且矩形
平面
,D,E分别是
,
的中点.
平面
.
(2)若
是等腰直角三角形,且
平面
,求平面
与平面
的夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75aea24647cd4d0b4b9aa513bf5457b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2533329cee82bcfe15b808839c0a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113c87d7b997847259f17ee8576ee44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3f9e8e58175cc46453515621e69193.png)
您最近一年使用:0次
2024-04-22更新
|
1250次组卷
|
2卷引用:河北省沧州市沧县中学2024届高三下学期3月高考模拟测试数学试题
名校
解题方法
2 . 如图,在几何体中,四边形
为菱形,对角线
与
的交点为O,四边形
为梯形,
.
,求证:
平面
;
(2)若
,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d70fb53a3bc46be3e6365f5ed26496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8a2235c2f2cf0e897201b6b5c3d22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5721abbe6afab23059a9391a64ec2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af142a6050b54e8b5777a085d4597481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce9fd745dfcffdb32c76c2b47ed20d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0038a080c58ec7e69c1c304ea19c1a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-04-15更新
|
1494次组卷
|
9卷引用:河北省衡水市故城县河北郑口中学2023-2024学年高一下学期5月月考数学试题
河北省衡水市故城县河北郑口中学2023-2024学年高一下学期5月月考数学试题浙江省金华市第一中学2023-2024学年高一下学期4月期中考试数学试题云南省保山市腾冲市第八中学2023-2024学年高一下学期4月期中考试数学试题河南省新乡市原阳县第一高级中学2023-2024学年高一下学期4月月考数学试题(已下线)6.5.2平面与平面垂直-【帮课堂】(北师大版2019必修第二册)(已下线)专题3.6空间直线、平面的垂直-重难点突破及混淆易错规避(人教A版2019必修第二册)(已下线)专题13.5空间平面与平面的位置关系-重难点突破及混淆易错规避(苏教版2019必修第二册)广东省茂名市信宜市第二中学2023-2024学年高一下学期5月月考数学试题河南省新乡市原阳县第一高级中学2023-2024学年高一下学期5月测试数学试题
名校
解题方法
3 . 如图,正四棱台
有内切球
,且
.
(1)设平面
平面
,证明
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8862c0bfcaf3818565fee2f99cf2dfea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/2715f3ff-1e6b-4a0d-9554-c02fcec36d0e.png?resizew=180)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522da06a9cb494a1e4496273108b68af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69861273f52724024c2bbf32f87c1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
您最近一年使用:0次
名校
4 . 如图,在直三棱柱
中,已知
.
(1)当
时,证明:
平面
.
(2)若
,且
,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/3f87880c188081c778716170e59782a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/2cb54b9b-a2d7-4c2b-bfcb-df62163cd52c.png?resizew=93)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3f9e8e58175cc46453515621e69193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
您最近一年使用:0次
2024-04-07更新
|
1186次组卷
|
5卷引用:河北省邢台市五岳联盟2024届高三下学期模拟预测数学试题
河北省邢台市五岳联盟2024届高三下学期模拟预测数学试题河南省部分省示范高中2024届高三下学期3月联考数学试卷贵州省安顺市部分学校2024届高三下学期二模考试数学试题云南省昆明市部分学校2024届高三下学期二模考试数学试题(已下线)云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试题变式题16-19
5 . 在三棱台
中,
为等边三角形,
,
平面
,
分别为
,
的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/7dffb745-2037-42ce-bbd9-a9f7eba59151.png?resizew=193)
(1)证明:平面
平面
;
(2)若
,设
为线段
上的动点,求
与平面
所成的角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a61472439de1ba85cfe33840b775f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/7dffb745-2037-42ce-bbd9-a9f7eba59151.png?resizew=193)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca81233fe44d2853df1a484580b6008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88e7df45acca3fc3d3da3370f0c32bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2024-03-24更新
|
986次组卷
|
2卷引用:河北省金科大联考2024届高三下学期3月质量检测数学试题
解题方法
6 . 如图,在多面体
中,底面
是边长为
的正方形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1b071579d7562d63aef9fc1a49b260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
平面
,动点
在线段
上,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/8ee0dd40-162e-4c2e-88c3-35abdcd2a35e.png?resizew=172)
![](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/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1b071579d7562d63aef9fc1a49b260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5d971c5140d79006ca2d066c2eaa81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/8ee0dd40-162e-4c2e-88c3-35abdcd2a35e.png?resizew=172)
A.![]() |
B.存在点![]() ![]() ![]() ![]() |
C.三棱锥![]() ![]() ![]() |
D.当动点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
7 . 如图,在平行六面体
中,
,
,
,
,点
为
中点.
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead0e8eadfdcefa334953e88864f424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7be9e552514a07e7f745666cb5b76b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b24a6fd9b4574e7808eafc57f8496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22391e2f16997bb4b99041f8543b2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104bf24922707215be95a860cd533940.png)
您最近一年使用:0次
2024-03-12更新
|
2927次组卷
|
9卷引用:专题04 立体几何
(已下线)专题04 立体几何辽宁省沈阳市五校联考2024届高三上学期期末数学试题(已下线)每日一题 第16题 不易建系 先证垂直(高三)(已下线)【一题多解】立体几何 新旧呼应湖南省长沙市雅礼中学2024届高三一模数学试卷江苏省常州市第一中学2024届高三下学期期初检测数学试题江西省宜春市丰城市第九中学2024届高三上学期期末考试数学试题辽宁省辽东十一所重点高中联合教研体2024届高三下学期高考适应性考试(一)数学试题(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题11-15
名校
8 . 已知
、
是不重合的两条直线,
、
是不重合的两个平面,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
9 . 如图,在圆柱
中,轴截面ABCD为正方形,点F是
的上一点,M为BD与轴
的交点.E为MB的中点,N为A在DF上的射影,且
平面AMN,则下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
A.![]() |
B.![]() |
C.![]() |
D.F是![]() |
您最近一年使用:0次
2024-03-08更新
|
1646次组卷
|
8卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题
河北省部分学校联考2024届高三下学期3月模拟(二)数学试题河北省衡水市枣强县衡水董子高级中学2023-2024学年高三下学期3月月考数学试题河北省石家庄市2024届高三下学期教学质量检测(一)数学试题河北省保定市清苑区清苑中学2023-2024学年高一下学期5月自测数学试题(已下线)专题 14 立体几何中线面垂直的判定问题(一题多解)(已下线)第1套 全真模拟篇 【模块三】(已下线)第四章 立体几何解题通法 专题四 投影变换法 微点3 投影变换法综合训练【培优版】(已下线)6.5.1 直线与平面垂直-同步精品课堂(北师大版2019必修第二册)
名校
10 . 如图,在梯形
中,
,
,
,
为等边三角形,平面
平面
,E为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/ca8deec9-fefe-4fc4-996f-bff155d5d0ab.png?resizew=189)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c935feadc24f95b0b137d0b82ef9b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/ca8deec9-fefe-4fc4-996f-bff155d5d0ab.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ae72f5e5891249caa10c43224da89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2024-03-02更新
|
777次组卷
|
2卷引用:河北省唐山市2023-2024学年高二上学期期末考试数学试题