1 . 如图,在正方体
中,点M在线段
(不包含端点)上运动,则下列判断中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/6a2ae746-9d42-4a38-97c0-64f1ff990906.png?resizew=169)
①
平面
; ②异面直线
与
所成角的取值范围是
;
③
平面
恒成立; ④三棱锥
的体积不是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/6a2ae746-9d42-4a38-97c0-64f1ff990906.png?resizew=169)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dbbf1a30ea54a46b903a9645debab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8419e07aa1a95c981372fc886bebc588.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3414bf337e4831721c7d894f6e125369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6557d0725272b008c5969c0a203aa10.png)
A.①③ | B.①② | C.①②③ | D.②④ |
您最近一年使用:0次
2021-10-24更新
|
1010次组卷
|
7卷引用:广西南宁市2022届高三高中毕业班上学期摸底测试数学(文)试题
广西南宁市2022届高三高中毕业班上学期摸底测试数学(文)试题(已下线)专题36 立体几何之根本-空间平行与垂直问题-备战2022年高考数学一轮复习一网打尽之重点难点突破(已下线)考点31 直线、平面平行与垂直的判定与性质-备战2022年高考数学典型试题解读与变式(已下线)热点06 空间位置关系的判断与证明-2022年高考数学【热点·重点·难点】专练(全国通用)(已下线)重难点03 空间向量与立体几何-2022年高考数学【热点·重点·难点】专练(新高考专用)江西省南昌市第十中学2021-2022学年高二下学期第一次月考数学(文)试题江西省南昌市第十中学2021-2022学年高二下学期第一次月考数学(理)试题
名校
解题方法
2 . 如图所示,
是半圆
的直径,
垂直于半圆
所在的平面,点
是圆周上不同于
的任意一点,
分别为
,
的中点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
A.![]() ![]() ![]() |
B.平面![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2022-06-16更新
|
784次组卷
|
3卷引用:广西浦北县第二中学2021-2022学年高一下学期期末模拟考试数学试题2
名校
解题方法
3 . 如图,平行四边形
所在平面与半圆弧
所在平面垂直,
是
上异于
,
的点,
为线段
的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/e3f9f03e-768c-433a-b8e8-66a2c9e4f5bf.png?resizew=233)
(1)证明:
平面
;
(2)证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2aabb3232e9ffabad9def25515cbdc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/e3f9f03e-768c-433a-b8e8-66a2c9e4f5bf.png?resizew=233)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a90c5466cb1f9810d2739a7634a4352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb23a04ac9df27fb987126e7ba0f6c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
您最近一年使用:0次
2022-07-06更新
|
627次组卷
|
3卷引用:广西柳州市柳州高级中学2023-2024学年高二上学期开学考试数学试卷
解题方法
4 . 如图,正方体
中,
、
分别是
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/65bf0f50-1254-40f1-b4bf-9a19187d295d.png?resizew=213)
(1)求证:
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/65bf0f50-1254-40f1-b4bf-9a19187d295d.png?resizew=213)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49644c4cdd8a0e9bb6241c625c4ae21e.png)
您最近一年使用:0次
2022-06-23更新
|
618次组卷
|
2卷引用:广西钦州市第四中学2022-2023学年高二上学期第二次学考模拟考试数学试题
名校
解题方法
5 . 如图,在四棱锥
中,
是以AD为斜边的等腰直角三角形,
,
,平面
平面ABCD,
,底面ABCD的面积为
,E为PD的中点.
(1)证明:
平面PAB;
(2)求直线CE与平面PAB间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/afa19c4a-8c93-4c07-b5ef-2b76a96b1fc2.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
(2)求直线CE与平面PAB间的距离.
您最近一年使用:0次
2023-10-17更新
|
260次组卷
|
2卷引用:广西玉林市博白县中学2023-2024学年高二上学期第一次月考数学试题
解题方法
6 . 如图,正四棱锥P-ABCD的高PO=4,
,
交
于
,
为侧棱
的中点.
(1)求证:
//平面
;
(2)求O到平面EBC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/28/35f76174-97d3-4e0c-8214-a46180fd5d61.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/415440adb63f3bc728ae315b5d77ce4b.png)
(2)求O到平面EBC的距离.
您最近一年使用:0次
10-11高一下·云南昆明·期末
名校
解题方法
7 . 如图,在直三棱柱
中,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2020/11/6/2587095510458368/2607613441253376/STEM/903dcf40c5fb48eab4b4d5327a5e1b6a.png?resizew=230)
求证:(1)
;
(2)
平面
.
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2020/11/6/2587095510458368/2607613441253376/STEM/903dcf40c5fb48eab4b4d5327a5e1b6a.png?resizew=230)
求证:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429228f882da65a8e0064c88d02b8e40.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cb62f4c1e0e023619922eb8a509c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
您最近一年使用:0次
2020-12-05更新
|
1367次组卷
|
21卷引用:广西百色市平果县第二中学2019-2020学年高一下学期期中考试数学试题
广西百色市平果县第二中学2019-2020学年高一下学期期中考试数学试题(已下线)云南省昆明三中10-11学年高一下学期期末考试数学(已下线)2011-2012学年贵州省遵义四中高二上学期期末考试理科数学(已下线)2011-2012学年云南省会泽县茚旺高级中学高二9月月考数学试卷2015-2016学年吉林省长春一三七中高一下学期期末联考数学试卷湖南省岳阳县一中2016-2017学年高一下学期期中考试数学试题四川省成都七中实验学校2016-2017学年高二下学期期中考试数学(理)试题四川省成都七中实验学校2016-2017学年高二下学期期中考试数学(文)试题北京市海淀清华附永丰学校2016-2017学年高二上学期期中考试数学试题河北省武邑中学2017-2018学年高一上学期期末考试数学试题北京市西城三十一中2017-2018学年高二上学期期中考试数学试题北师大版 全能练习 必修2 第一章 本章能力测评(一)A吉林省延边州汪清县四中2019-2020学年高一上学期第二次阶段考试数学试题吉林省梅河口市朝鲜族中学2019-2020学年高一上学期期末考试数学试题吉林省梅河口市三校2019-2020学年高一上学期期末联考数学试题四川省遂宁市安居区2020-2021学年高二上学期期中考试数学(文)试题四川省遂宁市安居区2020-2021学年高二上学期期中考试数学(理)试题(已下线)2.2.1 直线与平面平行的判定-2020-2021学年高一数学课时同步练(人教A版必修2)贵州省贵阳市清镇养正学校2019-2020学年高二上学期第一次月考数学(文)试题贵州省贵阳市清镇养正学校2019-2020学年高二上学期第一次月考数学(理)试题安徽省滁州市六校2019-2020学年高二上学期期中文科数学试题
名校
8 . 如图,四棱锥
中,
,
,
,
为正三角形,且平面
平面
,
为侧棱
的中点.
(1)求证:
平面
;
(2)若
,求直线
与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5ba108d7d2d4807f2c74a22e536fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/9/acc9586d-1f3a-4662-a2ea-854491b53538.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef7c2dbcbf5d871749c5939dccef729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb5f78b55cd826acbb962896c0086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-07-07更新
|
292次组卷
|
2卷引用:广西大学附属中学2023-2024学年高二上学期开学考试数学试题
解题方法
9 . 如图,在长方体
中,
,M,N分别为
,
的中点,AC与BD交于点O.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/785eb662-0bd7-48da-b3ce-7b3e05ad2d5d.png?resizew=195)
(1)证明:
平面
;
(2)证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0159041367660e750ace61115dc9b844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/785eb662-0bd7-48da-b3ce-7b3e05ad2d5d.png?resizew=195)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaa5e336f830a3e5cd60ff7a756f3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
您最近一年使用:0次
10 . 如图,棱长为4的正方体
的内切球为球
,
、
分别是棱
和棱
的中点,
在棱
上移动,则下列结论成立的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/a2d68d03-05f8-47b2-9cc0-1293129d481e.png?resizew=160)
A.存在点![]() ![]() |
B.对于任意点![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.过直线![]() ![]() ![]() |
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