1 . 如图,在四棱锥
中,
平面
,
为
的中点,
为
的中点,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/5139995d-07a7-49c5-b57d-657035ebbaa1.png?resizew=149)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.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/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ff87836403b4cf4f728d5ac4d2c87a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/5139995d-07a7-49c5-b57d-657035ebbaa1.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
您最近一年使用:0次
2 . 如图,点
为正方形
的中心,
为正三角形,平面
平面
,点
是线段
的中点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/d871e077-b1f2-43b6-b21e-292e773347e0.png?resizew=157)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c1acdd27cebb11e0266464b03b3afb.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/d871e077-b1f2-43b6-b21e-292e773347e0.png?resizew=157)
A.直线![]() ![]() | B.直线CD∥平面![]() |
C.直线![]() ![]() | D.二面角![]() |
您最近一年使用:0次
解题方法
3 . 如图,在长方体
中,
,点
为
的中点,点
是
上靠近
的三等分点,
与
交于点
.
(1)求证:
平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f4df0a32a910db7d39695ffd86665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/e50b0c89-8b2e-4a41-a9ab-d3abffa7e1df.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280247d7df395bb9ea78c51e67b458d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04731c2f37d21cd66d3f1554c24da16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff616a43f18947ab743ee1dcf27854.png)
您最近一年使用:0次
名校
4 . 如图,在三棱台
中,若
平面
,
为
中点,
为棱
上一动点(不包含端点).
(1)若
为
的中点,求证:
平面
.
(2)是否存在点
,使得平面
与平面
所成角的余弦值为
?若存在,求出
长度;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a65945b5b78ef143ab5d004bbb0625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9652a25569e1dc999a562df292d3770.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/3/73b46136-faba-4da4-9f06-66e4ef1d5ea1.png?resizew=168)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f845e74c18cdb2d6a80e0c0b4e85cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a3f5c4436466bed86c25c5f26ccbeb.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a3f5c4436466bed86c25c5f26ccbeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1145c162038df3c7184d9201c628e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
2023-10-17更新
|
1015次组卷
|
19卷引用:海南省海口市第一中学2023-2024学年高二上学期10月月考数学试题
海南省海口市第一中学2023-2024学年高二上学期10月月考数学试题湖南省长沙市长郡中学2023-2024学年高二上学期入学考试(暑假作业检测)数学试题江西省新余市实验中学2023-2024学年高二上学期开学摸底数学试题福建省莆田锦江中学2024届高三上学期第一次阶段(开学考)考试数学试题四川省成都外国语学校2023-2024学年高三上学期入学考试数学(理科)试卷重庆市第一中学校2023-2024学年高二上学期9月月考数学试题河南省商丘市宁陵县高级中学2023-2024学年高二上学期第一次考试数学试题河北省保定部分高中2023-2024学年高二上学期9月月考数学试题新疆维吾尔自治区塔城地区第一高级中学2023-2024学年高二上学期9月月考数学试题重庆市两江育才中学2023-2024学年高二上学期第一学月质量监测数学试题(已下线)考点巩固卷18 空间向量与立体几何(九大考点)辽宁省丹东市凤城市第一中学2023-2024学年高二上学期10月月考数学试题(已下线)考点13 立体几何中的探究问题 2024届高考数学考点总动员【练】山东省菏泽市第一中学2023-2024学年高二上学期第三次月考数学试题(已下线)第02讲 空间向量的应用(3)【名校面对面】2023-2024学年高二上学期第一次月考数学试题(已下线)专题09 空间向量中动点的设法2种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)专题06 二面角4种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)(已下线)通关练03 用空间向量解决距离、夹角问题10考点精练(58题) - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
解题方法
5 . 如图,几何体
为直四棱柱
截去一个角所得,四边形
是正方形,
,
,
为
的中点.
(1)证明:平面
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/f52eab6de89f4d4e69650e94e0968744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50943279ee6f0299b3725eecd77bafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/92945fb1-5f8e-41a6-817b-17959ae8853c.png?resizew=131)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803e2a6dd67c13a5fadb6548f9e1cec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0de3aeeff0480033ffd050165baf82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,底面
为菱形且边长为2,
,又
底面
,
为
的中点,
(1)求证:
;
(2)设
是
的中点,求证:
平面
.
![](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/e075468e7fb0bf30229aec01a7205977.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/15/b4d871d6-6112-4ca2-90d0-cbd433bb2876.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37c9f2fec8e6966125547af2628d9bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1925035dc7e4d98cd72f96fbb60ec2d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
您最近一年使用:0次
名校
7 . 如图,正四面体ABCD的顶点A,B,C分别在两两垂直的三条射线Ox,Oy,Oz上,则下列结论错误的为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/15/9f1607e7-d5f1-4c59-94a9-dc91a0e864ab.png?resizew=142)
A.![]() |
B.直线![]() |
C.直线AD与OB所成的角是45° |
D.二面角![]() |
您最近一年使用:0次
2023-09-10更新
|
220次组卷
|
6卷引用:海南省海口市第一中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
8 . 如图,在直三棱柱
中,
,D,E分别为
和
的中点.
(1)求证:
平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/f0e377f5-2599-4fa9-a87c-911f6e0cf3bb.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92bced6bf70db7229db85f2b10339431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a4075106569eec5da4cb17ddfb57ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
您最近一年使用:0次
2023-07-26更新
|
609次组卷
|
2卷引用:海南省海口市第一中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
9 . 已知四棱锥
中,
平面
,
,
,
,
为
中点.
(1)求证:
平面
;
(2)设平面
与平面
的夹角为45°,求P点到底面
的距离.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f86b6bb8d0612e06f5579090727379.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/2023/7/28/063db1d7-3989-4680-bc54-a6ca7697e64b.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8010e1a73f05117a278860c1c0c7f147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
10 . 如图所示,在多面体
中,底面
为矩形,且
底面
∥
.
(1)证明:
∥平面
.
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0591515beabb21e67a791e736774f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6848fee099124c81bf38006cf09d563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6fc14846b0eae51d8de30c0594641c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/0972d4c8-e699-4fd1-b983-99447549b360.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7090ad13cf3664c89cdb2288779a9669.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc83f34b5a3c1dc09d990ce4bdc8e078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7090ad13cf3664c89cdb2288779a9669.png)
您最近一年使用:0次