解题方法
1 . 如图,在四棱锥
中,底面
是矩形,
平面
,
,
,
是
上一点,且
.
(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/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/8c2753753faf2cb9a0003aa8e3945159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79a2100ec3a85bab03f88f23bd0b20e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/25/aa72e14d-cac5-4e65-aadf-b0ab3b4adc5c.png?resizew=151)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a7841fca64062a1f2112de9e696921.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
中,底面
是正方形,平面
底面
,侧棱
与底面所成的角为
.
(1)证明:平面
平面
;
(2)若平面
平面
,求二面角
的正弦值.
![](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/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/cc455b2f-c1c2-4d27-a6f8-9418a877d104.png?resizew=141)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2023-10-31更新
|
999次组卷
|
7卷引用:新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二上学期11月月考数学试题
解题方法
3 . 如图,在三棱柱
中,四边形
为菱形,
,四边形
为矩形,若
,
,
.
(1)求证:
平面
;
(2)求证:
平面
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332a341096f8b23cb90a60e03ea5009d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/80d419d1-c7b1-43d2-9aaf-01f707c0deaf.png?resizew=193)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f8b463fcecf0a757f386db56e074d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2023-10-26更新
|
218次组卷
|
3卷引用:新疆阿克苏地区柯坪县柯坪湖州国庆中学2023-2024学年高二上学期9月月考数学试题
新疆阿克苏地区柯坪县柯坪湖州国庆中学2023-2024学年高二上学期9月月考数学试题陕西省榆林市定边县第四中学2024届高三上学期第四次月考数学(文)试题(已下线)考点9 垂直的判定与性质 2024届高考数学考点总动员【练】
名校
解题方法
4 . 如图,在棱长为1的正方体
中,点
为线段
上的动点(含端点),下列四个结论中,正确的有( )
![](https://img.xkw.com/dksih/QBM/2023/10/23/3352214410592256/3352889834610688/STEM/04636d5b6b06410993caf984bdeaa514.png?resizew=172)
![](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/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/2023/10/23/3352214410592256/3352889834610688/STEM/04636d5b6b06410993caf984bdeaa514.png?resizew=172)
A.存在点![]() ![]() ![]() |
B.存在点![]() ![]() ![]() ![]() |
C.存在点![]() ![]() ![]() |
D.不存在点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
5 . 如图,
是四棱柱,侧棱
底面
,底面
是梯形,
,
.
(1)求证:平面
平面
;
(2)E是底面
所在平面上一个动点,是否存在点E使得
与平面
夹角的正弦值为
?若存在,求点E到平面
距离的最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.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/ce519312a849963b376c202c3f9d7cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6155f82a6f64b20085976cea9b64193.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/25/2cd5a2a5-827a-4eed-adb1-f186fc61dc7f.png?resizew=140)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9578aee1ffa7a74c04debf1679b068d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)E是底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea50e734d1cb88f847b241ce9397be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
您最近一年使用:0次
2023-10-23更新
|
553次组卷
|
5卷引用:新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二上学期第三次月考数学试题
新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二上学期第三次月考数学试题广东省广州四中2023-2024学年高二上学期月考数学试题(已下线)湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题变式题19-22(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】(已下线)考点16 立体几何中的最值问题 2024届高考数学考点总动员【练】
名校
6 . 如图所示,在四棱锥
中,侧面
底面
,侧棱
,
,底面
为直角梯形,
,
,
,
为
的中点.
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/e302bba1-4804-467a-962b-93e3542c78d0.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeebdf3d00c146a1b4d220909d7573c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb5255e2159617505e0c87d01437a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-10-18更新
|
538次组卷
|
2卷引用:新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二上学期10月月考数学试题
名校
7 . 如图,直三棱柱
的所有棱长都是2,
分别是
的中点.
(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/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98842968c75427c940b34de391a3a778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d06f8edd1a1f18ca2dae700c6a29ab4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/23/2b6a3e38-044b-4132-8316-b256242a0019.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
您最近一年使用:0次
2023-10-03更新
|
770次组卷
|
2卷引用:新疆维吾尔自治区喀什地区巴楚县2023-2024学年高二上学期9月月考数学试题
名校
解题方法
8 . 如图所示,AC为圆O直径,B为圆O上不同于A、C的点,P不在圆O平面内,E为线段BC中点.
(1)求证:
∥平面PAB;
(2)若平面
平面ABC,且
,求证:
平面POE.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/1/3a2f1793-7b2b-4b59-8061-3648ada04628.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb96e0331eebe80ed1ff610faf531fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
您最近一年使用:0次
2023-09-27更新
|
430次组卷
|
3卷引用:新疆维吾尔自治区乌鲁木齐市第十一中学2024届高三上学期12月月考数学试题
新疆维吾尔自治区乌鲁木齐市第十一中学2024届高三上学期12月月考数学试题江苏省淮安市淮阴中学2023-2024学年高二上学期期初调研测试数学试题(已下线)专题8.8 空间中的线面位置关系大题专项训练【七大题型】-举一反三系列
名校
9 . 如图,已知正方体
的棱长为1,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/ff345f42-b874-4719-9de8-258a76019d50.png?resizew=172)
A.![]() |
B.![]() ![]() |
C.平面![]() ![]() ![]() |
D.点![]() ![]() ![]() |
您最近一年使用:0次
2023-09-27更新
|
372次组卷
|
4卷引用:新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
10 . 如图,在直三棱柱
中,
,
,直线
与平面
所成角的正弦值为
,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d150134e5018f74fc4e8a016ced5f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a408ceb4c78bf63ed9dc85451d0839d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/12/6e89f2b9-75d3-4451-9b3b-5392004a6f9e.png?resizew=148)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-09-11更新
|
1194次组卷
|
5卷引用:新疆昌吉市第一中学2023-2024学年高二上学期9月月考数学试题