名校
解题方法
1 . 如图,在棱长为1的正方体
中( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/af7c62fc-8866-4f0f-8b67-71f35eaee264.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/af7c62fc-8866-4f0f-8b67-71f35eaee264.png?resizew=163)
A.![]() ![]() ![]() |
B.二面角![]() ![]() |
C.![]() ![]() ![]() |
D.点![]() ![]() ![]() |
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2022-12-13更新
|
798次组卷
|
3卷引用:黑龙江省海伦市第二中学2023届高三上学期期末数学试题
名校
解题方法
2 . 如图,在多面体
中,四边形
是边长为2的正方形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/4c33a3b4-cac8-4a4b-b79f-cb8575dd1c97.png?resizew=140)
(1)求证:平面
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580523898a4086a8278c08df33ea6190.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/4c33a3b4-cac8-4a4b-b79f-cb8575dd1c97.png?resizew=140)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d62d30d732c3c6ee3f0dd66d7059356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
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3 . 在三棱锥
中,
平面
,点
在棱
上且是
的外心(三角形三边的垂直平分线的交点叫三角形的外心即外接圆的圆心),点
是
的内心(三角形的内心是三角形三条角平分线的交点即内切圆的圆心),
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/647a6ab7-7ba9-4cd1-a97c-d27eb3e4261a.png?resizew=167)
(1)求证:平面
平面
;
(2)求二面角
的正弦值.
![](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/a45914248db0766b62e5017a3d29937f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbf9680f74a9ac5d934304654ce2771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/647a6ab7-7ba9-4cd1-a97c-d27eb3e4261a.png?resizew=167)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a45fd0b63ff6f429b236ad8939cb22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376122641840d08823d2f7d663ca70d2.png)
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4 . 如图,在五面体
中,
,
平面
,
.已知
,
,
,且
.
平面
;
(2)求平面
与平面
的夹角的余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ab061ed9ec918926f1defceb85924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9b0421e0b4d74b22df706578b74a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563f3214a5f5ce732a91be9038ee0468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15e58659e6ee4d93650e2edb6d6f7ff.png)
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2022-11-15更新
|
145次组卷
|
3卷引用:黑龙江省绥化市绥棱县第一中学2023-2024学年高三上学期9月月考数学试题
5 . 如图,在多面体
中,上、下底面平行且均为矩形,相对的侧面与同一底面所成的二面角大小相等,侧棱延长后相交于E,F两点,上、下底面矩形的长、宽分别为c,d与a,b,且a>c,b>d,两底面间的距离为h.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/ec9a9a6d-8a31-4c5b-a286-a510f114a143.png?resizew=242)
(1)求侧面
与底面
所成二面角的大小;
(2)证明:
;
(3)在估测该多面体的体积时,经常运用近似公式
来计算,已知它的体积公式是
,试判断
与V的大小关系,并加以证明.
注:与两个底面平行,且到两个底面距离相等的截面称为该多面体的中截面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/ec9a9a6d-8a31-4c5b-a286-a510f114a143.png?resizew=242)
(1)求侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f67eaf0a9ead191ae26e84dd0d12b6.png)
(3)在估测该多面体的体积时,经常运用近似公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a02fce86b05e431bd95aa97ac29312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb43e591021b79f00642d5ca2d2bf738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac758a10c1fc71d638145aeb8dcd3834.png)
注:与两个底面平行,且到两个底面距离相等的截面称为该多面体的中截面.
您最近一年使用:0次
2022-11-09更新
|
207次组卷
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2卷引用:黑龙江省鸡西市密山市高级中学联考2023-2024学年高二上学期12月期末数学试题
名校
解题方法
6 . 在正方体
中,
分别是
的中点,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/6211742e-c82c-4d9e-9093-950a388fbdfb.png?resizew=173)
![](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/238aafef2a6748f15278acb0475ee72b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/6211742e-c82c-4d9e-9093-950a388fbdfb.png?resizew=173)
A.四边形![]() |
B.直线![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.平面![]() ![]() ![]() |
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2022-11-06更新
|
932次组卷
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5卷引用:黑龙江省哈尔滨师范大学附属中学2022-2023学年高二上学期期中考试数学试题
黑龙江省哈尔滨师范大学附属中学2022-2023学年高二上学期期中考试数学试题黑龙江省伊春市铁力市马永顺中学2022-2023学年高二上学期期末数学试题浙江省温州新力量联盟2022-2023学年高二上学期期中联考数学试题(已下线)第33讲二面角的几何求法(已下线)专题8.17 立体几何初步全章综合测试卷(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)
名校
7 . 在平行四边形
中,
,沿
将
折起,使二面角
的大小为
,设点
在平面
上的射影为点
.
![](https://img.xkw.com/dksih/QBM/2022/10/25/3095493252677632/3096158509572096/STEM/1d5b119118a34778b6b8d06a181794f7.png?resizew=417)
(1)当
为何值时,三棱锥
的体积最大?最大值为多少?
(2)当
时,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8679764b2abafd810da5e7bde240dcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282d4a8c3476b2b81e3fd73898e64539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2022/10/25/3095493252677632/3096158509572096/STEM/1d5b119118a34778b6b8d06a181794f7.png?resizew=417)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb01ad3508483c8929d5bf3fb8d5fc2c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
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8 . 在正方体ABCD-A1B1C1D1中,下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/8b990916-f9e6-4562-b563-f23c7e2c0815.png?resizew=211)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/8b990916-f9e6-4562-b563-f23c7e2c0815.png?resizew=211)
A.直线BD与A1D 所成的角为45° |
B.异面直线BD与AD1所成的角为60° |
C.二面角A-B1C-C1的正弦值为![]() |
D.二面角A-B1C-C1的正弦值为![]() |
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2022-10-18更新
|
682次组卷
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8卷引用:黑龙江省哈尔滨德强学校2022-2023学年高二(宏志班)上学期期中考试数学试题(B卷)
名校
9 . 棱长为4的正方体
中,E,F分别为棱
,
的中点,若
,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72545bef56c4e32d1b76489bd32c3842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17230625e72d3a9c6d72ff61019ff61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f83044285fd2454d070d0ba68c2bdab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7265a048c572531048c11147b04f4e.png)
A.三棱锥![]() |
B.二面角![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
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2022-10-17更新
|
546次组卷
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4卷引用:黑龙江省哈尔滨德强学校2022-2023学年高二(清北AB班)上学期期中考试数学试题(A卷)
名校
10 . 如图,正方体
的棱长为
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/7d23bbb7-f319-4328-a51c-f180968314ee.png?resizew=178)
(1)求点
到平面
的距离;
(2)求二面角
的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/7d23bbb7-f319-4328-a51c-f180968314ee.png?resizew=178)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb2a344518d4d3a9b443129a869ab44.png)
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