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1 . 对下列命题:①两两相交的三条直线确定一个平面;②已知直线
、
和平面
,若
、
与
所成的角相等,则
;③若两个平面平行,则其中一个平面内的直线必平行于另一个平面;④三个两两垂直的平面的相应交线也两两垂直,其中真命题的序号是______ .(填上所有真命题序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff4e42856fa5f6a4e12993e53b065e3.png)
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2 . 设
是两个不同的平面,
是直线且
.“
”是“
”的__________ 条件.(填“充分不必要”、“必要不充分”、“充要”、“不充分不必要”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539a38ada26356d73024fb8533449c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c6d37467a5c995d71e49408503927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
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解题方法
3 . 在棱长为2的正方体
中,点M是对角线
上的点(点M与A、
不重合),则下列结论正确的是______________ .(请填写序号)
①存在点M,使得平面
平面
;
②存在点M,使得
平面
;
③若
的面积为S,则
;
④若
、
分别是
在平面
与平面
的正投影的面积,则存在点M,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/ff785f15-c66b-43ee-bd82-a02f45c1820f.png?resizew=157)
①存在点M,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba49eb8ddd4dd38c1f994ccec93430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
②存在点M,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce447afe4b0bb57a844b2c103b55fc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42910d271417cc2435d0affa6c85afd5.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce447afe4b0bb57a844b2c103b55fc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd78e9156dcf6db93f6cbcc5b43b14.png)
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解题方法
4 . 已知四棱雉
的底面是边长为4的正方形,
面
,点
、
分别是
、
的中点,
为
上一点,且
,
为正方形
内一点,若
面
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d26466d9b36d3f3e1035952c130421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d99fdec0ccdbe208b6b42cc297216c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffff2b4b4417e6109f0975b44dc05bdf.png)
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解题方法
5 . 如图,在四棱锥
中,底面
为平行四边形,
分别为
的中点,点
在棱
上,且
平面
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c91fc8ae6c0a05a1a057f00c00cb27.png)
______ .
![](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/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f9499c94f38a54cb12092c7a58c19a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d300fc3d421b67abca2167f99f14d635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c91fc8ae6c0a05a1a057f00c00cb27.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/11/86583d91-bce0-4424-86f8-84992c31f1c0.png?resizew=180)
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6 . 如图,正方体
的棱长为2,点
是线段
的中点,点
是正方形
所在平面内一动点,若
平面
,则
点轨迹在正方形
内的长度为________ .
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d28074ee5af1441242700388b3a9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/b35bdb17-a0e5-4dbd-a3a7-bb1a043f6dfc.png?resizew=151)
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解题方法
7 . 已知正方体
的棱长为2,点
,
分别是棱
,
的中点,若动点
在正方形
(包括边界)内运动,且
平面
,则线段
的长度范围是_________ .
![](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/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/editorImg/2023/6/10/31e0ab07-7992-4b5a-868c-da4221b9de3e.png?resizew=152)
您最近一年使用:0次
2023-05-20更新
|
514次组卷
|
4卷引用:山东省潍坊市安丘市国开中学2022-2023学年高二下学期6月月考数学试题
名校
解题方法
8 . 如图,矩形
中,
,
为边
的中点,将
沿直线
翻折至
的位置.若
为线段
的中点,在
翻折过程中(
平面
),给出以下结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/75579b14-d042-4f3f-94ed-2310a0e41d23.png?resizew=198)
①存在
,使
;
②三棱锥
体积最大值为
;
③直线
平面
.
则其中正确结论的序号为_________ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.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/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8588e18e27bfebf7c81c7e3c7efb1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/75579b14-d042-4f3f-94ed-2310a0e41d23.png?resizew=198)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2181c78134c310f746eab44b9124e63b.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb79f948d408ab4fb6708bde172c5e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b9f96b8ecc3cb000bb2f030809f225.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c70966a318ef8ecf874257f5c5e5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
则其中正确结论的序号为
您最近一年使用:0次
2023-03-13更新
|
365次组卷
|
3卷引用:河南省许昌市鄢陵县职业教育中心(升学班)2022-2023学年高二下学期期中考试数学试题
河南省许昌市鄢陵县职业教育中心(升学班)2022-2023学年高二下学期期中考试数学试题宁夏六盘山高级中学2023届高三第一次模拟数学(文)试题(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)
名校
解题方法
9 . 如图,在棱长为4的正方体
中,
是
的中点,点
是侧面
上的动点.且
平面
,则线段
长度的取值范围是________ .
![](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/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3123da0313d458c833e82aaa234b9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/c9ab69f8-e06a-44c7-9d15-9870d01887f7.png?resizew=179)
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2023-01-18更新
|
681次组卷
|
4卷引用:四川省南充市嘉陵第一中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
10 . 下面四个正方体中,点A、B为正方体的两个顶点,点M、N、P分别为其所在棱的中点,能得出
平面
的图形序号是______ .(写出所有符合条件的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52173c8cc44246823c2bee21a783b731.png)
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2023-02-06更新
|
1829次组卷
|
15卷引用:上海市第十中学2022-2023学年高二上学期12月月考数学试题
上海市第十中学2022-2023学年高二上学期12月月考数学试题(已下线)10.4 平面与平面间的位置关系(第1课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)四川省南充市阆中市阆中中学校2023-2024学年高二上学期11月月考数学试题山东省烟台第一中学2023-2024学年高二下学期2月月考数学试题沪教版(2020) 必修第三册 高效课堂 第十章 10.3直线与平面位置关系(1)(已下线)8.5.3 平面与平面平行(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)第八章 立体几何初步(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(人教A版2019必修第二册)(已下线)必修二全册综合测试卷(基础篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)专题8.10 空间直线、平面的平行(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)湖南省长沙市宁乡市2022-2023学年高一下学期期末数学试题(已下线)模块二 专题4 立体几何中的平行与垂直的位置关系 基础卷A(已下线)模块二 专题7 立体几何中的平行与垂直的位置关系 基础卷A(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】(已下线)第10讲 8.5.3 平面与平面平行-【帮课堂】(人教A版2019必修第二册)(已下线)8.5空间直线、平面的平行——课后作业(基础版)