解题方法
1 . 已知直线与平面
,
,
,能使
的充分条件是( )
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() ![]() |
您最近一年使用:0次
2 . 如图,在四棱锥中,平面
平面ABCD,
,
,
,
,
,
,
.
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(2)在线段PB上是否存在点M,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5865d488a9cf1181016fd2e866177cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8180b12d96caf2e6b3ca28a474185e41.png)
您最近一年使用:0次
2023-04-01更新
|
830次组卷
|
4卷引用:陕西省安康中学2023届高三下学期3月质量检测文科数学试题
陕西省安康中学2023届高三下学期3月质量检测文科数学试题四川省仁寿县铧强中学2023届高三三模文科数学试题(已下线)专题06空间位置关系的判断与证明(已下线)专题06 立体几何 第一讲 立体几何中的证明问题(分层练)
名校
解题方法
3 . 如图所示的在多面体中,
,平面
平面
,平面
平面
,点
分别是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/30/9edec392-47cf-4f57-bff3-eb7956c25941.png?resizew=185)
(1)证明:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
平面
;
(2)若
,求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d55ec5203187112176740b5c2c6058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3919bf9dce67c9522d2f3878b69cac40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/30/9edec392-47cf-4f57-bff3-eb7956c25941.png?resizew=185)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b986dcc94536991b5800d2dd6b3d68c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
2023-03-30更新
|
3755次组卷
|
4卷引用:广东省部分学校2023届高三下学期3月模拟数学试题
名校
解题方法
4 . 如图,在棱长为1的正方体
中,M是
的中点,点P是侧面
上的动点,且.
平面
,则线段MP长度的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f66702d72329bdfd455f4fe3e724cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-03-25更新
|
1690次组卷
|
4卷引用:山东省枣庄市2023届高三下学期第二次模拟考试数学试题
5 . 如图,在四棱锥中,底面
是边长为
的菱形,
分别是
的中点,
平面
,
,且
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67825108ba67284ae24eb4780ba65531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2023-03-24更新
|
258次组卷
|
2卷引用:青海省西宁市大通回族土族自治县2023届高三一模数学(文)试题
名校
解题方法
6 . 如图所示,长方体
中,
,O是
的中点,直线
交平面
于点M,则下列结论错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/26005fa9-0149-4583-aac2-1ce7c135e329.png?resizew=156)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06df159fbc33b70abf9d96c4ef278acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/26005fa9-0149-4583-aac2-1ce7c135e329.png?resizew=156)
A.A,M,O三点共线 |
B.![]() |
C.直线![]() ![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2023-03-21更新
|
821次组卷
|
4卷引用:河南省2022-2023学年高三下学期核心模拟卷(中)文科数学(二)试题
河南省2022-2023学年高三下学期核心模拟卷(中)文科数学(二)试题青海省西宁市大通回族土族自治县2023届高三第二次模拟考试文科数学试题(已下线)重难点专题03 空间直线平面的垂直-【同步题型讲义】四川省广安第二中学校2023-2024学年高三上学期第二次月考理科数学试题
2023·全国·模拟预测
名校
解题方法
7 . 如图1,在梯形
中,
,
,
,
,
,线段
的垂直平分线与
交于点
,与
交于点
,现将四边形
沿
折起,使
,
分别到点
,
的位置,得到几何体
,如图2所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/5936c8b2-ae86-4b3e-8825-c2f1af0ac12e.png?resizew=273)
(1)判断线段
上是否存在点
,使得平面
平面
,若存在,求出点
的位置;若不存在,请说明理由.
(2)若
,求平面
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/d730ae4307db56b47849c3a19dedfb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/85227bdb3148e51177d6e26523cbffd6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/5936c8b2-ae86-4b3e-8825-c2f1af0ac12e.png?resizew=273)
(1)判断线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864efbb42ff7e695cb6bc00bbc0a8107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c262229271a283b8293fe3f4f57f97e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1769cd4d629d8ffb00e8511cfda306b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ed2f4c77adb6528231eecd735512c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c262229271a283b8293fe3f4f57f97e1.png)
您最近一年使用:0次
2023-03-18更新
|
806次组卷
|
6卷引用:2023年普通高等学校招生全国统一考试数学猜题卷(九)
(已下线)2023年普通高等学校招生全国统一考试数学猜题卷(九)黑龙江省哈尔滨市第九中学校2023届高三第四次模拟数学试题四川省成都市树德中学2022-2023学年高二下学期4月月考数学(理)试题(已下线)数学(江苏卷)四川省仁寿第二中学2022-2023学年高二下学期第二次教学质量检测理科数学试题(已下线)单元高难问题01探索性问题(各大名校30题专项训练)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)
名校
8 . 已知
,
是两条不同的直线,
,
,
是三个不同的平面,则下列正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-03-18更新
|
1245次组卷
|
5卷引用:天津市新华中学2024届高三下学期数学学科统练2
解题方法
9 . 如图,在四棱锥
中,底面
是边长为
的菱形,
,
,
分别是
,
,
的中点,
平面
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/17/c5e54af3-2f07-4ace-9505-188c2698cb67.png?resizew=280)
(1)证明:
平面
;
(2)求二面角
的大小.
![](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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443ebca856f5c88869a8c3906c6b97b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db39823f5ae71572164b66ad0a31a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/17/c5e54af3-2f07-4ace-9505-188c2698cb67.png?resizew=280)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67825108ba67284ae24eb4780ba65531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
2023-03-16更新
|
480次组卷
|
2卷引用:青海省西宁市大通回族土族自治县2023届高三一模数学(理)试题
10 . 在棱长为4的正方体
中,点
,
分别是棱
,
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
A.![]() | B.![]() ![]() |
C.平面![]() ![]() | D.点![]() ![]() ![]() |
您最近一年使用:0次
2023-03-10更新
|
1344次组卷
|
6卷引用:河北省唐山市2023届高三一模数学试题
河北省唐山市2023届高三一模数学试题河北省邢台市名校联盟2023届高三下学期3月模拟(二)数学试题湖南省长沙市周南中学2023届高三二模数学试题江西省吉安市永丰县永丰中学2022-2023学年高二下学期期中考试数学试题(已下线)2.4.4 向量与距离(同步练习)-【素养提升—课时练】2022-2023学年高二数学湘教版选择性必修第二册检测(基础篇)(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)