名校
解题方法
1 . 如图正方形ACDE所在平面与平面ABC垂直,M是CE和AD的交点,且
,
.
(1)求证:
平面EBC;
(2)求锐二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/b1404641-05c8-4b55-bcd1-bc9a16d235fd.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
(2)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a351d71fa01d3f5920e374a8ee7b524.png)
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2023-12-11更新
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225次组卷
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7卷引用:四川省泸州市泸县第五中学2020-2021学年高二上学期第二次月考数学(理)试题
名校
解题方法
2 . 在棱长为1的正方体
中,
为线段
的中点,设平面
与平面
的交线为
,则点A到直线
的距离为____________ .
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475d9dbaac17f65044500bd8fad9a135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-08更新
|
272次组卷
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6卷引用:四川省泸州市泸县第一中学2024届高三上学期期末数学(理)试题
四川省泸州市泸县第一中学2024届高三上学期期末数学(理)试题广东省深圳市五校联考2023-2024学年高二上学期12月段考数学试题(已下线)6.3 空间向量的应用 (4)(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)第3章 空间向量及其应用 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)3.4.2 求距离(六大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
解题方法
3 . 如图,
的二面角的棱上有
,
两点,直线
,
分别在这个二面角的两个半平面内,且都垂直于
.已知
,则
长度为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd40fa72911ae508ef169ddf4fb640dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2023/12/6/3383501951713280/3383563381473280/STEM/7d915a3d0255452aac4b3940b15615a2.png?resizew=136)
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2023-12-06更新
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560次组卷
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17卷引用:四川省泸县第一中学2020-2021学年高二上学期第一次月考数学(理)试题
四川省泸县第一中学2020-2021学年高二上学期第一次月考数学(理)试题山东省济宁市2016-2017学年高二下学期期末考试理数试题山东省曲阜师范大学附属中学2016-2017学年高二下学期期末考试数学(理)试题【全国百强校】安徽省淮北市第一中学2018-2019学年高二下学期第二次月考数学(理)试题湖南省常德市2019-2020学年高二上学期期末数学试题湖北省沙市中学、郧阳中学、恩施高中、随州二中2019-2020学年高二上学期第三次月考数学试题福建省尤溪县2018-2019学年普通高中高二上学期半期数学(理)试题湖北省黄冈市黄梅国际育才高级中学2019-2020学年高二上学期9月月考数学试题河北省石家庄市四中2021-2022学年高二上学期第一次月考数学试题福建省将乐县第一中学2021-2022学年高二上学期第一次月考数学试题内蒙古霍林郭勒市第一中学2021-2022学年高二上学期期中考试数学(理科)试题河南省平顶山市郏县第一高级中学2021-2022学年高二下学期开学收心考试数学(理)试题陕西省咸阳市实验中学2023-2024学年高二上学期第二次月考数学试题(已下线)专题 01 空间基底及综合应用(2)(已下线)专题 01 空间基底及综合应用(2)河南省南阳市唐河县2023-2024学年高二上学期期末质量检测数学试题(已下线)第14讲 8.6.3平面与平面垂直(第1课时 )-【帮课堂】(人教A版2019必修第二册)
名校
4 . 在平行六面体
中,底面
是边长为2的正方形,侧棱
的长为3,且
,则
为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d1a9810e0c13807aacc5660b857fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6aff8f132c42eac7795112c24c62b39.png)
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2023-12-03更新
|
215次组卷
|
2卷引用:四川省泸州市2023-2024学年高二上学期期末模拟考试数学试题
名校
5 . 如图,在多面体
中,平面
平面
,
平面
和
均为正三角形,
为线段
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cfd6b6a7e911d10d1a4bed9ca5e749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46a5ce5c10b7a419055abf43764fce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176385d91d5e29324fce4a932eff6a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9926397d0839f1a02946828dc348a7d.png)
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2023-11-30更新
|
228次组卷
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3卷引用:四川省泸州市泸县第五中学2023-2024学年高二上学期期末数学试题
四川省泸州市泸县第五中学2023-2024学年高二上学期期末数学试题重庆市永川北山中学校2023-2024学年高二上学期期中考试数学试题(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题11-15
6 . 如图所示四棱锥
中,
底面
,四边形
中,
,
,
,
.
(1)求证:
平面
;
(2)求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81981fd7b343f4fe2db8f36eb66c1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/a97b2abf-b2a2-4c88-a593-6c6f5a35ab82.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
名校
解题方法
7 . 在三棱锥
中,
平面
,
,且
,则三棱锥
的外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81981fd7b343f4fe2db8f36eb66c1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-29更新
|
708次组卷
|
3卷引用:四川省泸州市古蔺县蔺阳中学校2023-2024学年高二上学期期中考试理科数学试题
四川省泸州市古蔺县蔺阳中学校2023-2024学年高二上学期期中考试理科数学试题江西省宜春市清江中学2023-2024学年高二上学期期中数学试题(已下线)第二章 立体几何中的计算 专题六 几何体的外接球、棱切球、内切球 微点2 长方体切割体及其模型综合训练【基础版】
解题方法
8 . 三棱柱的侧棱垂直于底面,所有的棱长都为
,顶点都在一个球面上,则该球的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 如图,在正方体
中,
、
、
、
分别是棱
、
、
、
的中点,则下列结论中正确的有________ .
①
平面
②
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
③
、
、
、
四点共面 ④
、
、
、
四点共面
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/c52f37a0-b2bb-47f8-8823-fc343da9abad.png?resizew=157)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcafa398cc6b6079883e7ad153eb62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331da51a299acaaafa61551d0ebd3e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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10 . 如图,已知在棱长为2的正方体
中,点E,F,H分别是
,
,
的中点,点G是
上的动点,下列结论中正确的有________________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/cf1e3d64-9f44-4305-9b4d-4d194ea209e0.png?resizew=138)
①
平面ABH ②
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad7c7bdb5c5cfa477eb4f5ea57d2b.png)
③直线EF与
所成的角为
④三棱锥
的体积最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/cf1e3d64-9f44-4305-9b4d-4d194ea209e0.png?resizew=138)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cae8fd28341fc24851e03e9ba1d4e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad7c7bdb5c5cfa477eb4f5ea57d2b.png)
③直线EF与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996bf3d35b6763cbc1a423b13a9df2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c9299f4c44108e7808d6270fe6f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
您最近一年使用:0次