1 . 如图,在四棱锥
中,底面
是边长为2的正方形,且
,
,点
分别为
的中点.
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5c72eac8cd820bb448215c2d462415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930e85bc9f73e86cfb6ce9b076433f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2 . 如图,多面体
中,四边形
为菱形,
,
,
,
.
平面
;
(2)当
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860cd26630a3172fa079ead357dac4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daee8baa62b5b8d5db41eab0d360ee51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ff7bf8ffc8a04186e3e13c1a6d5ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630cbaf628064c66436caa267201bc55.png)
您最近一年使用:0次
2024-03-08更新
|
1848次组卷
|
5卷引用:陕西省西安市第一中学2024届高三第十次模拟考试数学(文)试题
陕西省西安市第一中学2024届高三第十次模拟考试数学(文)试题四川省大数据学考联盟2024届高三第一次质量检测数学(文科)试题四川省绵阳市三台中学校2024届高三下学期第二学月测试文科数学试题(已下线)专题07 空间直线﹑平面的垂直(二)-《知识解读·题型专练》(人教A版2019必修第二册)(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)
名校
3 . 如图,将正四棱柱
斜立在平面
上,顶点
在平面
内,
平面
,点
在平面
内,且
.若将该正四棱柱绕
旋转,
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db768f2ad30b15e6d533056ee6332ea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e7842ec06f4f0c29b7ca67810e68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
2024-03-07更新
|
470次组卷
|
6卷引用:陕西省西安市第一中学2024届高三下学期第九次模拟考试文科数学试题
4 . 如图所示,在三棱锥
中,
,
,点O、D分别是
、
的中点,
底面
.
(1)求证:
平面
;
(2)当k取何值时,二面角
的余弦值为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61085b97b88eb1f5e5cf196f9d846053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/99b8c7b8-223e-4d39-bd0b-2a78abdc0008.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377ca47ae9b5ea2a870b6c0b12cfa010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)当k取何值时,二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
您最近一年使用:0次
5 . 如图,在矩形ABCD中,
,E,F分别为BC,AD中点,将
沿直线AE翻折成
与B、F不重合,连结
,H为
中点,连结CH,FH,则在翻折过程中,下列说法中不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b124087e8e0f003f15224ecc3c983228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266cd441f6f470c652b52275adb9d260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48495275addca4fb0c95c5dcb1dc2389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
A.CH的长是定值 |
B.在翻折过程中,三棱锥![]() ![]() |
C.当![]() ![]() ![]() |
D.点H到面![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知直线
和平面
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde22242618f18849cfa42d31a5979b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8444d63d1ca92651c62fe9b220859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea730233033e2fca0bce6a369a32582f.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-02-12更新
|
1344次组卷
|
8卷引用:陕西省西安中学2024届高三模拟考试(五)理科数学试题
(已下线)陕西省西安中学2024届高三模拟考试(五)理科数学试题浙江省金丽衢十二校2023-2024学年高三上学期第一次联考数学试题(已下线)考点4 条件的判断 --2024届高考数学考点总动员【讲】(已下线)13.2.3 直线与平面的位置关系(2)-【帮课堂】(苏教版2019必修第二册)(已下线)专题04 立体几何(已下线)8.5.1直线与平面平行河北省石家庄一中2023-2024学年高二下学期第一次月考数学试题(已下线)专题05 立体几何初步客观题热点题型(2) -期末真题分类汇编(江苏专用)
名校
7 . 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)
您最近一年使用:0次
2024-02-06更新
|
1030次组卷
|
6卷引用:陕西省商洛市2024届高三第四次模拟检测数学(理科)试题
陕西省商洛市2024届高三第四次模拟检测数学(理科)试题湖南省长沙市2024届高三上学期新高考适应性考试数学试卷(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
解题方法
8 . 如图,在四棱锥
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/adcb658e-3739-475d-ab40-db553701daba.png?resizew=144)
(1)求证:
;
(2)若四棱锥
的体积为12,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ed4f6bc8c7f08e80b194b867b0092d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f72c935697ef9ceb633a15b90b19ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/adcb658e-3739-475d-ab40-db553701daba.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2024-01-25更新
|
391次组卷
|
2卷引用:陕西省汉中市汉台区2024届高三下学期教学质量检测考试数学(理)试题
9 . 如图,在四棱锥
中,
平面
,四边形
为平行四边形,
为棱
上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/08fb60a6-a606-45fe-ac16-47cb3fd7e62f.png?resizew=173)
(1)求证:
;
(2)若
,求二面角
的大小.
![](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/ea5fe3373780926c7af50b7441449b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/08fb60a6-a606-45fe-ac16-47cb3fd7e62f.png?resizew=173)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e384e0ffc3d599303b77ee2a12221e.png)
您最近一年使用:0次
解题方法
10 . 如图,在三棱柱
中,平面
平面
,侧面
为菱形,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/3c88ec61-88d3-40ef-8856-b8c54936b7c9.png?resizew=181)
(1)证明:
;
(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/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e34345885421ac2f5aff094534cba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/3c88ec61-88d3-40ef-8856-b8c54936b7c9.png?resizew=181)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab9dcd6116087d8f6a933d17d815e58.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3625c3dc03287d1bf53966f7e319c867.png)
您最近一年使用:0次