名校
1 . 如图1,在矩形
中,
,
,将
沿矩形的对角线
进行翻折,得到如图2所示的三棱锥
.
时,求
的长;
(2)当平面
平面
时,求平面
和平面
的夹角的余弦值.
![](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/1ffc2817fa590affb5a760a25dc65308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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2024-02-06更新
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6卷引用:湖南省长沙市2024届高三上学期新高考适应性考试数学试卷
湖南省长沙市2024届高三上学期新高考适应性考试数学试卷陕西省商洛市2024届高三第四次模拟检测数学(理科)试题(已下线)模块4 二模重组卷 第2套 复盘卷(已下线)第5讲:立体几何中的动态问题【练】(已下线)专题3 翻折变换 模型转化 练江西省景德镇市乐平中学2023-2024学年高二下学期4月期中考试数学试题
2 . 设
是两条不同的直线,
是两个不同的平面,则下面说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2024-02-29更新
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5卷引用:湖南省平江县第三中学等多校联考2023-2024学年高二普通高中学业水平合格性考试仿真模拟(专家卷一)数学试题
湖南省平江县第三中学等多校联考2023-2024学年高二普通高中学业水平合格性考试仿真模拟(专家卷一)数学试题湖南省2024届高三数学新改革提高训练五(九省联考题型)辽宁省沈阳市2024届高三教学质量监测(三)数学试题(已下线)热点6-1 线线、线面、面面的平行与垂直(6题型+满分技巧+限时检测)(已下线)第二套 艺体生新高考全真模拟 (三模重组卷)
2023·全国·模拟预测
3 . 如图,在多面体ABCDEF中,四边形ABCE和四边形CDEF是全等的直角梯形,且这两个梯形所在的平面相互垂直,其中
.
平面BCD;
(2)求平面BCD和平面ABF的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0b4ee0295c2c55e4a6c76d473b5ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
(2)求平面BCD和平面ABF的夹角的余弦值.
您最近一年使用:0次
名校
4 . 如图,在四棱锥
,
,
,E为PC的中点.
平面PAD;
(2)若平面
平面ABCD,求直线AB与平面PCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c143b614d0a3a873d8dfa89a812402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813a9bd80b817e87e790b0ce0f102719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
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2023-11-15更新
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4卷引用:湖南省长沙市长郡中学2024届高考适应考试(四)数学试题
名校
5 . 如图,在三棱柱中
,平面
平面
,四边形
是矩形,四边形
是平行四边形,且
,
,
,以
为直径的圆经过点
.
(1)求证:
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535770901287f244911b42412533d4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faffe3765c15f53305516895aa595a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/7087e2c1-7a1f-4d10-8df6-3c00045aa924.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2023-10-27更新
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7卷引用:湖南省郴州市2024届高三一模数学试题
湖南省郴州市2024届高三一模数学试题河南省洛阳市洛宁县第一高级中学2023-2024学年高三上学期11月月考数学试题江西省宜春市宜丰县宜丰中学创新部2024届高三上学期期中数学试题宁夏银川市第二中学2024届高三上学期年级统练四数学(理)试题(已下线)第一章 点线面位置关系 专题二 空间垂直关系的判定与证明 微点3 直线与平面垂直的判定与证明【基础版】辽宁省沈阳市翔宇中学2023-2024学年高二上学期第二次月考测试数学试题(已下线)湖南省郴州市2024届高三一模数学试题变式题17-22
名校
6 . 如图,在四棱台
中,平面
平面ABCD,底面ABCD为正方形,
,
.
(1)求证:
平面
.
(2)点
在直线
上,且
平面MCD,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd14966183389b10618cbe33fd777407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b12ce74b68cf02f948c8c1c7f4b5922.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/1/21bd3c0b-5d89-4e21-86ad-b19e1be00538.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e89acc2b46a2ff0e61c894c56382b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2cda9e5690d90d24c318895db59a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
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2023-05-29更新
|
694次组卷
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4卷引用:湖南省郴州市宜章县四校2023届高三模拟数学试题
解题方法
7 . 如图,
是等腰直角三角形,
,四边形
是直角梯形,
,
,且
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/8aa4f890-4631-4fcd-a9b2-f1d65151bafd.png?resizew=160)
(1)求证:
;
(2)若点E是线段
上的一动点,问点E在何位置时,三棱锥
的体积为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f9fba8a4098c1a0515286eb8d616dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae17686725a5ecc001c809cfc35d1429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4685bc53d11be0f30476c377d76561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1801ddbdf49f88c1800b422f108f0ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb5012f6c70a1e98d682b6d021fadd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/8aa4f890-4631-4fcd-a9b2-f1d65151bafd.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804c0e2a375b5f4ff1c420532968efc3.png)
(2)若点E是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fea520be511f0bca09d795851b0fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eba0bd4a60613ffd02e08bdd1a1eebe.png)
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2023-05-16更新
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3卷引用:湖南省衡阳师范学院祁东附属中学2023届高三下学期考前适应性考试数学试题
湖南省衡阳师范学院祁东附属中学2023届高三下学期考前适应性考试数学试题宁夏银川一中、昆明一中2023届高三联合二模考试数学(文)试题(已下线)高一数学下学期期末模拟试题02(平面向量、解三角形、复数、立体几何、概率统计)-【同步题型讲义】
解题方法
8 . 如图,四棱锥
内,
平面
,四边形
为正方形,
,
.过
的直线
交平面
于正方形
内的点
,且满足平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/16/eb940b24-7f74-4bc9-b486-331bfc5ffc93.png?resizew=137)
(1)当
时,求点
的轨迹长度;
(2)当二面角
的余弦值为
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd051fedb6691e2183e658f1fe487ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392469b357b12b998528499929366c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/16/eb940b24-7f74-4bc9-b486-331bfc5ffc93.png?resizew=137)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057b210a3422696c23c63acb9ae98c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1a4b8e6a3514ac93b69042d1f9553b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5c3c0ab9b7ba915604ed7e4e19254f.png)
您最近一年使用:0次
解题方法
9 . 在棱长为
的正方体
中,动点
在平面
上运动,且
,三棱锥
外接球球面上任意一点
到点
到的距离记为
,当平面
与平面
夹角的正切值为
时,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce066003c0a1f0879cbca2f32802e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd5048110640575a5e01d4c36e22744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecc884f5b4dc9622e90e1303bc481f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce066003c0a1f0879cbca2f32802e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2213b575a7cfaffcdf91885005c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
名校
10 . 如图,在三棱柱
中,
是边长为2的等边三角形,
,平面
平面ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/559f3292-9480-4bf7-b09b-2c7da36aba40.png?resizew=218)
(1)证明:
;
(2)若E为
的中点,直线
与平面
所成的角为45°,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252143a7b900d33862f60b2536f6a8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/559f3292-9480-4bf7-b09b-2c7da36aba40.png?resizew=218)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696da912e610974f0f437876b3d34ee3.png)
(2)若E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
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2023-04-16更新
|
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5卷引用:湖南省长沙市长郡中学2023届高三二模数学试题