解题方法
1 . 如图,在三棱锥
中,
平面
,平面
平面
,
,
,
为线段
的中点.
;
(2)求三棱锥
的体积.
![](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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bae7599ad243c12d94325ad917f0a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
名校
2 . 如图所示,半圆柱的轴截面为平面
,
是圆柱底面的直径,
为底面圆心,
为一条母线,
为
的中点,且
.
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07956720a50ff238c0766a5d58d00e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e346722774c2a1913719928e352d78ef.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa768881697b8d4c246b511b63e134c.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
3 . 如图①,在直角梯形
中,
,
,
,
,
,
,
分别在边
上,四边形
为正方形,将
沿着边
旋转,使得
,如图②.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/20bf03eb-c5aa-47b8-af18-42755b8c370e.png?resizew=330)
(1)求证:
平面
;
(2)
是棱
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9186e4574ffe28e673724fcb019db208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424269ceef173843aae76e39ecdf6111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33804bda15aa245e3a64dcc2e4c0b24f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97bb57534d77c2355aef18c9105c189d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d8b64ae5ebb831b1d03316e89f4aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96f3af5833b0cab2dff3e615c8790ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a618e2fa885d453e050c21bc05f8fed4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/20bf03eb-c5aa-47b8-af18-42755b8c370e.png?resizew=330)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ab0137fe07fc29af8eae62bb8a8495.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
4 . 已知四棱锥
如图所示,平面
平面
,四边形
为菱形,
为等边三角形,直线
与平面
所成角的正切值为1.
;
(2)若点
是线段AD上靠近
的四等分点,
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.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/5830322dd2824ed012a68f1a2bd9c742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5578cd49feb7c846f087b041371c3875.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/e5da631296d53a08d56fb5f9bec2376c.png)
您最近一年使用:0次
2024-01-02更新
|
856次组卷
|
6卷引用:2024年全国高考名校名师联席命制数学(文)信息卷(十一)
(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(十一)江西省上饶市玉山县第二中学2024届高三上学期12月月考数学试题(已下线)第16讲 拓展一:立体几何中空间角的问题和点到平面距离问题-【帮课堂】(人教A版2019必修第二册)(已下线)专题8.9 空间角与空间距离大题专项训练-举一反三系列(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)(已下线)11.4.2平面与平面垂直-同步精品课堂(人教B版2019必修第四册)
解题方法
5 . 如图,已知
垂直于梯形
所在的平面,矩形
的对角线交于点
为
的中点,
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
平面
;
(2)在线段
上是否存在一点
,使得
与平面
所成角的大小为
?若存在,求出
的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc6fd59aca9984b6e13354749339823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d10d2e0d8b2152bfc2877c7cfd5169.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/5dc2b64e-d36a-45d0-a05a-fc61566854b1.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffee8b7eff437080a0936d837ceabe95.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
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名校
6 . 如图,四棱锥
的底面是等腰梯形,
,
,
,
,
为棱
上的一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/9/9534b7f4-29d2-4fc7-b8de-93c3c3b20d6b.png?resizew=155)
(1)证明:
;
(2)若二面角
的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa9254b9703c6d3935ef8b3b8e36b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9641d01140939c44450bf39773272af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf84ccef60fa8fd62bb826acfc4cd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/9/9534b7f4-29d2-4fc7-b8de-93c3c3b20d6b.png?resizew=155)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f304789d5bcf31d9998fd4d920cd157.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1d9f040e7c4c6e4d9e8c0ed4f44984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e23ab2a5db0d58b522f1e2699bfe60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a386b370ffb5739049b3391112b5d2.png)
您最近一年使用:0次
2023-05-08更新
|
2240次组卷
|
6卷引用:陕西省商洛市2023届高三三模理科数学试题
名校
7 . 如图,三棱柱
的侧棱与底面垂直,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/9/11/3064419340214272/3064754319769600/STEM/f52bca12f2c74f7f92f98ac4cde795c9.png?resizew=215)
(1)求证:
;
(2)求
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/b6dfcb0a6104a9be3ee2d8e4c9e5991b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2022/9/11/3064419340214272/3064754319769600/STEM/f52bca12f2c74f7f92f98ac4cde795c9.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4cdc3a083d1263634d510f172dab09.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc7e774e4ae40c23bf4ceed179230ca.png)
您最近一年使用:0次
2022-09-12更新
|
3827次组卷
|
6卷引用:安徽省合肥市第十中学2022-2023 学年高三上学期学情检测一数学试题
名校
8 . 如图,在四棱锥
中,侧面
是边长为
的正三角形且与底面垂直,底面
是菱形,且
,
为棱
上的动点,且
.
![](https://img.xkw.com/dksih/QBM/2022/9/2/3057811122692096/3057845507432448/STEM/571fea07919a4b8789b6a773132ad9e7.png?resizew=189)
(1)求证:
为直角三角形;
(2)试确定
的值,使得平面
与平面
夹角的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fceddfa42f8cac1903c31d822cc1d66e.png)
![](https://img.xkw.com/dksih/QBM/2022/9/2/3057811122692096/3057845507432448/STEM/571fea07919a4b8789b6a773132ad9e7.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(2)试确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
您最近一年使用:0次
2022-09-02更新
|
2372次组卷
|
2卷引用:浙江省湖州市湖州中学2024届高三上学期第一次质量检测数学试题
名校
9 . 在圆锥PO中,高
,母线
,B为底面圆O上异于A的任意一点.
![](https://img.xkw.com/dksih/QBM/2022/4/14/2958094116044800/2959245912768512/STEM/910e6a9c-8820-46c4-b2b2-9fcbf48d850f.png?resizew=389)
(1)当
时,过底面圆心O作
所在平面的垂线,垂足为H,求证:
;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://img.xkw.com/dksih/QBM/2022/4/14/2958094116044800/2959245912768512/STEM/910e6a9c-8820-46c4-b2b2-9fcbf48d850f.png?resizew=389)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25490c72ad1b9968e6be5c5f6b268ab3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d162c29b1e484cfc87350dd68f00b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb92d6ab1b9a520e272f3649f35ab07a.png)
您最近一年使用:0次
2022-04-16更新
|
1832次组卷
|
5卷引用:甘肃省2022届高三第二次高考诊断考试数学(理)试题
甘肃省2022届高三第二次高考诊断考试数学(理)试题吉林省白山市抚松县第一中学2023届高考模拟预测数学试题宁夏回族自治区固原市西吉中学2024届高三上学期第五次模拟考试数学(理)试题(已下线)秘籍06 空间向量与立体几何(理)-备战2022年高考数学抢分秘籍(全国通用)(已下线)回归教材重难点03 空间向量与立体几何-【查漏补缺】2022年高考数学(理)三轮冲刺过关
解题方法
10 . 如图,在三棱锥D—ABC中,G是△ABC的重心,E,F分别在BC,CD上,且
,
.
![](https://img.xkw.com/dksih/QBM/2022/3/16/2937568463167488/2938680845516800/STEM/a9bb2de0d4534065ba668f42fc8fe81c.png?resizew=181)
(1)证明:平面
平面ABD;
(2)若
平面ABC,
,
,
,P是线段EF上一点,当线段GP长度取最小值时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91928fb7fc49b70ffd1f3a7dbeb566f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ad6b6519a55c2a502b9a94d3b514b4.png)
![](https://img.xkw.com/dksih/QBM/2022/3/16/2937568463167488/2938680845516800/STEM/a9bb2de0d4534065ba668f42fc8fe81c.png?resizew=181)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51daddc16eddbdf70ab3c15a28f6286b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
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