名校
解题方法
1 . 如图,在棱长为2的正方体
中,
,
,
分别为
,
,
的中点,则( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2856d51e-d206-4871-b9fa-d987a0021dde.png?resizew=145)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2856d51e-d206-4871-b9fa-d987a0021dde.png?resizew=145)
A.直线![]() ![]() | B.直线![]() ![]() |
C.直线![]() ![]() ![]() | D.点![]() ![]() ![]() |
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7卷引用:广东省广州市执信中学2023届高三上学期11月月考数学试题
名校
2 . 在空间中,设
是不同的直线,
表示不同的平面,则下列命题正确的是 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0877194ab8760f54c35527177b03ff93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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2卷引用:山东省聊城第一中学2023-2024学年高一下学期第二次阶段性测试数学试题
名校
解题方法
3 . 如图,在正方体
中,点
分别是棱
上的动点.给出下面四个命题
①直线
与直线
平行;
②若直线
与直线
共面,则直线
与直线
相交;
③直线
到平面
的距离为定值;
④直线
与直线
所成角的最大值是
.
![](https://img.xkw.com/dksih/QBM/2021/1/22/2641875529039872/2642253787734016/STEM/7b5fd5655a8842b7b4f29dced9f2cd46.png?resizew=265)
其中,真命题的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d426a84258d99282df25c0216777545.png)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://img.xkw.com/dksih/QBM/2021/1/22/2641875529039872/2642253787734016/STEM/7b5fd5655a8842b7b4f29dced9f2cd46.png?resizew=265)
其中,真命题的个数是( )
A.1 | B.2 | C.3 | D.4 |
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4卷引用:安徽省亳州市涡阳县育萃高级中学2020-2021学年高二下学期第一次月考数学(理)试题
名校
解题方法
4 . 如图所示,在棱长为a的正方体ABCD -A1B1C1D1中,E是棱DD1的中点,F是侧面CDD1C1上的动点,且B1F∥平面A1BE,则F在侧面CDD1C1上的轨迹的长度是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/dfe3a333-bcbf-458b-ae78-8e1fa68d5d92.png?resizew=164)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/dfe3a333-bcbf-458b-ae78-8e1fa68d5d92.png?resizew=164)
A.a | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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|
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18卷引用:江西省赣州市赣县区第三中学2020-2021学年高二(零班,奥数班)九月月考数学(文)试题
江西省赣州市赣县区第三中学2020-2021学年高二(零班,奥数班)九月月考数学(文)试题广东省汕头市陈店实验中学2020-2021学年高二上学期第一次月考数学试题浙江省金华市浙江师大附属东阳花园外国语学校2020-2021学年高二上学期第一次质量检测数学试题北京市西城区第十三中学2021-2022学年高一数学6月线上测试试题辽宁省铁岭市昌图县第一高级中学2022-2023学年高一下学期6月月考数学试题2019年10月广东省广州市天河区高考数学一模(文)试题2020届广东省佛山市第一中学高三上学期期中数学(文)试题2020届辽宁省沈阳市东北育才学校高中部高三第六次模拟数学(文)试题巩固练08 空间直线、平面的平行-2020年【衔接教材·暑假作业】新高二数学(2019人教版)浙江省嘉兴一中2019-2020学年高二上学期10月月考数学试题(已下线)第33讲 空间中的平行关系-2021年新高考数学一轮专题复习(新高考专版)(已下线)第29练 空间点、线、面的位置关系-2021年高考数学(文)一轮复习小题必刷(已下线)8.5.3 平面与平面平行(分层练习)-2020-2021学年高一数学新教材配套练习(人教A版2019必修第二册)(已下线)专题8-1 立体几何中的轨迹问题-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)沪教版(2020) 必修第三册 精准辅导 第11章 单元测试(已下线)增分专题五 空间几何体轨迹问题苏教版(2019) 必修第二册 过关斩将 第13章 专题强化练4 平面与平面的位置关系(已下线)第七章 重难专攻(七)?立体几何中的综合问题(核心考点集训)
2020·全国·模拟预测
名校
解题方法
5 . 如图,正方体
的棱长为
,
是棱
的中点,
是四边形
内一点(包含边界).若
平面
,且线段
长度的最小值为
,则
( )
![](https://img.xkw.com/dksih/QBM/2021/1/12/2634687191252992/2635482147602432/STEM/79218ce1-5d91-4207-afe5-7c0f489b4dd6.png?resizew=221)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://img.xkw.com/dksih/QBM/2021/1/12/2634687191252992/2635482147602432/STEM/79218ce1-5d91-4207-afe5-7c0f489b4dd6.png?resizew=221)
A.![]() | B.2 | C.![]() | D.3 |
您最近一年使用:0次
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|
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|
7卷引用:江西省宜春市万载中学2021-2022学年高一下学期第二次月考数学(文)试题
江西省宜春市万载中学2021-2022学年高一下学期第二次月考数学(文)试题(已下线)2021年全国高中名校名师原创预测卷 文科数学 (第九模拟)(已下线)2021年全国高中名校名师原创预测卷 文科数学 全国卷Ⅰ(第八模拟)新高考2021届高三考前保温热身模拟卷数学试题(二)江西省上饶市重点高中2022-2023学年高二上学期开学考试数学试题湖北省襄阳市第四中学2022-2023学年高二上学期新起点考试数学试题广东仲元中学2022-2023学年高二上学期期中数学试题
解题方法
6 . 如图,四边形
是边长为1的正方形,
平面
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/2020/12/29/2624681803489280/2628295185555456/STEM/077deb1e7b2c4bfb8b748b0cef15a898.png?resizew=160)
(1)求证:
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb92a5e7dc942c44d0f6d7f3906ff804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c611de332ba0c529d633a6cfe5240d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5254a8bb97154dc16c9435ef00ff5818.png)
![](https://img.xkw.com/dksih/QBM/2020/12/29/2624681803489280/2628295185555456/STEM/077deb1e7b2c4bfb8b748b0cef15a898.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d11e0a64470aac58556c3c99c18be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ac7cf883a6e586d06e3f33875bd95b.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,已知正方体
的棱长为
,
、
分别是棱
、
的中点.若点
为侧面正方形
内(含边界)动点,且
平面
,则点
的轨迹长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/5df58cb6-0a81-4e9b-91d7-6a276a8cc68c.png?resizew=146)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b668b5c01e0b1a529cc4e3efb2e9057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/5df58cb6-0a81-4e9b-91d7-6a276a8cc68c.png?resizew=146)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-01-02更新
|
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|
5卷引用:山西省运城市高中联合体2020-2021学年高二上学期12月调研测试数学(文)试题
解题方法
8 . 点
,
分别是棱长为
的正方体
中棱
,
的中点,动点
在正方形
(包括边界)内运动,若
面
,则
的长度的最大值是( )
![](https://img.xkw.com/dksih/QBM/2020/12/25/2621717853773824/2626968853897216/STEM/99c7238d-fbd7-47ad-bc3f-6f8533858214.png?resizew=292)
![](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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97f5b48031341b45f8285179cdeacc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://img.xkw.com/dksih/QBM/2020/12/25/2621717853773824/2626968853897216/STEM/99c7238d-fbd7-47ad-bc3f-6f8533858214.png?resizew=292)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
9 . 如图,正方体
,棱长为4,
分别为
上的点,点
为
中点,且
.
![](https://img.xkw.com/dksih/QBM/2020/12/24/2621246615035904/2623745744273408/STEM/8d5cb1c5-518a-4978-b1a1-f962684be1dd.png)
(1)当
时,求证:
平面
;
(2)当
为何值时,三棱锥
的体积最大?,并求出最大值是多少.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3355e2fa0ac6c675f02ee36c3ced4f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582fca0c1348fbbf733909680affa238.png)
![](https://img.xkw.com/dksih/QBM/2020/12/24/2621246615035904/2623745744273408/STEM/8d5cb1c5-518a-4978-b1a1-f962684be1dd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5d46cc6946821619e937d12d30dc83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5a44046c8232c8b81924036c6ba9ed.png)
您最近一年使用:0次
名校
解题方法
10 . (如图1)在直角梯形
中,
,
,
,
,
,点
在
上,且
.将
沿
折起,使得平面
平面
(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/967965e2-1efd-40e4-b065-0bd7bc1a29d2.png?resizew=364)
(1)求证:
;
(2)在线段
上是否存在点
,使得
平面
?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40560ea08d6cd8c1d4d9661ee6faaa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/967965e2-1efd-40e4-b065-0bd7bc1a29d2.png?resizew=364)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c897a54f2e36bc4b52fba74b41c89d2d.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93651f094df56f6b87fbd1d12c7a3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e49382868c1bbbc8ccfc1fddf981fd.png)
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