解题方法
1 . 如图,在正方体
中,
,过点
作平面
与
垂直,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/27/9cb9594f-babf-4764-9ed8-98dce0bf0e7f.png?resizew=169)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962ddfa6a45e5588279c2a93f142924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/27/9cb9594f-babf-4764-9ed8-98dce0bf0e7f.png?resizew=169)
A.![]() | B.点![]() ![]() ![]() |
C.![]() ![]() | D.![]() ![]() ![]() |
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解题方法
2 . 如图,在三棱锥V—ABC中,M,N分别为的棱VA,VB的中点,
,
,△ABC和△ACV都是等腰直角三角形,平面VAC⊥平面ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/12/6f1cd4f0-54e9-4693-95b0-a6e79b02a3b6.png?resizew=159)
(1)求证:AB//平面CMN;
(2)求证:AB⊥平面VBC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1dde4586a8952301ea04575abe3416.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/12/6f1cd4f0-54e9-4693-95b0-a6e79b02a3b6.png?resizew=159)
(1)求证:AB//平面CMN;
(2)求证:AB⊥平面VBC.
您最近一年使用:0次
解题方法
3 . 在正方体
中,点P在线段
上运动,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
A.直线AB与![]() |
B.直线![]() ![]() |
C.异面直线AP与![]() ![]() |
D.三棱锥![]() |
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名校
解题方法
4 . 如图,四棱锥
中,
为正方形,
为
的中点,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/7/1/3013276741443584/3016525308485632/STEM/3f4c3c4b1e374c9e921e9712b94b9e74.png?resizew=235)
(1)证明:
平面
;
(2)证明:
.
(3)求三棱锥
的体积.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.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/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70e550fa3c5aaf1b9c28f36fd5ed5d1.png)
![](https://img.xkw.com/dksih/QBM/2022/7/1/3013276741443584/3016525308485632/STEM/3f4c3c4b1e374c9e921e9712b94b9e74.png?resizew=235)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd79c634922b5a533d80555e8c979ce.png)
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2022-07-06更新
|
538次组卷
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3卷引用:广西梧州市2021-2022学年高一下学期期末检测数学试题
名校
5 . 如图,在正三棱柱
中,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/68c20bf2-0209-4201-b186-c060d2015bbb.png?resizew=244)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
.
(2)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602e5c7566b69aee8a7ddd18f825bf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cfad1ba71a78d8f415335cde2f8c52.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/68c20bf2-0209-4201-b186-c060d2015bbb.png?resizew=244)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcfe69b939fd1c271747fe9d37ccdf9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f4d9c3f1e496cc3fa3401ffaedd7e6.png)
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2022-06-29更新
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4卷引用:广西南宁市普通高中联考2021-2022学年高一下学期期末考试数学试题
名校
6 . 如图,正方体
的棱长为2,E是棱
的中点,F是侧面
上的动点,且满足
平面
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ea211a573491409cb60f9fbe9a65cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
A.平面![]() ![]() ![]() |
B.点F的轨迹长度为![]() |
C.存在点F,使得![]() |
D.平面![]() ![]() ![]() |
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2022-05-28更新
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10卷引用:广西南宁市第二中学2022-2023学年高一下学期期末考试数学试题
广西南宁市第二中学2022-2023学年高一下学期期末考试数学试题三湘名校教育联盟2021-2022学年高一下学期5月联考数学试题重庆外国语学校(即四川外国语大学附属外国语学校)2021-2022学年高一下学期6月月考数学试题(已下线)江苏省扬州市2021-2022学年高一下学期期末适应性测试数学试题(已下线)高一下期末模拟测试卷二-【单元测试】(苏教版2019必修第二册)河南省濮阳市华龙区第一高级中学2022-2023学年高一下学期6月月考数学试题河南省郑州市郑州中学2022-2023学年高一下学期联考模拟数学试题(三)广西南宁市第二中学2023-2024学年高二下学期期中考试数学试卷广东省广州市黄埔区广州科学城中学2023-2024学年高一下学期5月月考数学试题(已下线)专题22 立体几何中的轨迹问题-1
名校
解题方法
7 . 图,在正三棱柱
中,O为
与
的交点,M为
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/967cb39e-51f9-4598-8df3-d77f92111cbc.png?resizew=191)
(1)证明:
平面
;
(2)若G为线段FC上一动点,在平面
上是否存在一点N,使得
平面
恒成立?若存在,请找出点N位置并证明
平面
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393ebfea258a58906706888f0d6f2582.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/967cb39e-51f9-4598-8df3-d77f92111cbc.png?resizew=191)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1211fdbcc2a4a36e24b4e6c5c920bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)若G为线段FC上一动点,在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e6c97d975d4b04061715c41c00e1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b14cf4977ee2dac0bd5b0fca4dadc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e6c97d975d4b04061715c41c00e1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b14cf4977ee2dac0bd5b0fca4dadc3.png)
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2022-05-13更新
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5卷引用:广西桂平市麻垌中学2021-2022学年高一下学期期中考试数学试题
广西桂平市麻垌中学2021-2022学年高一下学期期中考试数学试题福建省龙岩市非一级达标校2021-2022学年高一下学期期中联考数学试题河北省邢台市南和区第一中学2021-2022学年高一下学期第三次月考数学试题福建省厦门外国语学校2021-2022学年高一下学期期中考试数学试题(已下线)第一章 点线面位置关系 专题一 空间平行关系的判定与证明 微点1 空间平行关系的判定与证明【培优版】
名校
解题方法
8 . 如图,四棱柱
中,底面ABCD是菱形,
,
平面ABCD,E为
中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/febec444-e341-426e-bade-a0dc5bd777f2.png?resizew=181)
(1)求证:
平面
;
(2)求三棱锥
的体积;
(3)在
上是否存在点M,满足
平面
?若存在,求出AM的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/febec444-e341-426e-bade-a0dc5bd777f2.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89006cac018a9875f65ed7bd429c61bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48e2f18c4c61dfcc908827ac3c8a204.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c23ea8141b89b3c737ce64d3be380f.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3414bf337e4831721c7d894f6e125369.png)
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2022-04-30更新
|
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5卷引用:广西南宁市宾阳中学2021-2022学年高一下学期期末考试数学试题
广西南宁市宾阳中学2021-2022学年高一下学期期末考试数学试题广东省清远市重点中学2021-2022学年高一下学期期中数学试题云南省昆明市嵩明县2021-2022学年高一下学期期中考试数学试题(已下线)专题08 立体几何中的平行与垂直问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)广西柳州市第三中学2023-2024学年高二上学期开学数学试题
名校
解题方法
9 . 在五面体
中,面
为平行四边形,
,且
,
为棱
的中点.
的中点为
,证明:平面
平面
;
(2)请画出过点
,
,
的平面与平面
的交线
,证明
.
![](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/06772d7ccc921f77319c503c23326be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10546e0e0d462be05cd1a6b78b727624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c8a954ff05adb6dd5fed003f79f104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)请画出过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc46bcc6cb032ca29f32962b8aa5c9c2.png)
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2022-04-23更新
|
798次组卷
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2卷引用:广西百色市平果市铝城中学2023-2024学年高一下学期4月月考测试数学试卷
名校
解题方法
10 . 如图,已知正四棱锥
中,O为底面
对角线的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/3612a9ff-8f8d-43c2-8a67-85083b2c65a5.png?resizew=176)
(1)求证:
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/3612a9ff-8f8d-43c2-8a67-85083b2c65a5.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2022-03-28更新
|
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2卷引用:广西贺州市2021-2022学年高一下学期期末质量检测数学试题