解题方法
1 . 如图,在三棱锥
中,
为等边三角形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/00d56d60-34b5-45dc-b004-8f048c25db0f.png?resizew=162)
(1)求证:平面
平面
;
(2)点
是棱
上的动点,当直线
与平面
所成角的正弦值为
时,求
点的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed595a5db9bcb4e0f877b453cbbe4541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/00d56d60-34b5-45dc-b004-8f048c25db0f.png?resizew=162)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c7a937699f989b685f285041434000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2 . 如图,在正三棱锥
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/faad7182-0a6d-48e2-9b88-a44672a510d0.png?resizew=155)
(1)求证:四边形
为矩形.
(2)若四边形
为正方形,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5471f78107efbfb8bb29aed493cbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbd464c5adc6b6450a98f28f545ae2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/faad7182-0a6d-48e2-9b88-a44672a510d0.png?resizew=155)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17dea6aa2b6d8362542af3a7a8d55c08.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17dea6aa2b6d8362542af3a7a8d55c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
3 . 如图,已知三棱锥
中,
,
,O为AC的中点,点N在边BC边上,且
,
(1)证明:BO⊥平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
(2)求二面角
的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34af872b64f8dd0e43ff81c4ca6c3f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60759a4d86c9a5529677b90d0d1f238.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/b7d571b5-e928-403e-b151-7a24ed036183.png?resizew=161)
(1)证明:BO⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2edd3e5b926b9bb6e34ef4ada50914.png)
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名校
解题方法
4 . 在棱长为1的正方体
中,球
以点
为球心,棱
为半径,则平面
被球
截得的区域面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775df7ba0dc94c15e9e706194a463f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
5 . 如图,在四棱锥
中,底面
为正方形,
底面
,
,点
为线段
的中点,点
为线段
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/547d5c8b-6f6e-4f71-ae8c-54ecb756edca.png?resizew=164)
(1)求证:平面
平面
.
(2)试确定点
的位置,使平面
与平面
所成的锐二面角为
.
![](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/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/547d5c8b-6f6e-4f71-ae8c-54ecb756edca.png?resizew=164)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)试确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
您最近一年使用:0次
2023-11-26更新
|
154次组卷
|
12卷引用:福建省福州市2019-2020学年高三上学期期末质量检测数学(理)试题
福建省福州市2019-2020学年高三上学期期末质量检测数学(理)试题福建省福州华侨中学2023届高三上学期第二次考试数学试题2020届湖南省长沙市长望浏宁四县高三下学期4月联考理科数学试题广东省佛山市第一中学2022届高三上学期12月月考数学试题山东省实验中学2021-2022学年高三下学期3月诊断训练数学试题广西桂林、崇左、贺州、河池、来宾市2022届高三联合高考模拟考试数学(理)试题广东省揭阳市惠来县第一中学2021-2022学年高二下学期第一次段考数学试题广东省惠州市(惠阳中山中学、龙门中学、惠州仲恺中学)三校2023届高三上学期第一次质量检测数学试题河南省南阳市第二中学校2022-2023学年高二上学期12月月考数学试题湖北省宜昌市部分省级示范高中2023-2024学年高二上学期11月月考数学试卷广东省韶关市广东北江实验学校2023-2024学年高二上学期第二次月考(12月)数学试题(已下线)模块三 专题4 大题分类练(立体几何)拔高能力练
23-24高三上·福建·期中
6 . 如图,在四棱锥
中,
为等边三角形,
为
的中点,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/e45bb5a3-01f3-4e09-b043-d57738a5b746.jpg?resizew=182)
(1)证明:平面
平面
;
(2)若
,
,
,直线
与平面
所成角的正弦值为
,求三棱锥
的体积.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/e45bb5a3-01f3-4e09-b043-d57738a5b746.jpg?resizew=182)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75463911a178c1425bf65787589ad03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9f2a9caa28a5266b12188771c6ace4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f35614aff055b98b76ca262f64e629d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf91e7449e859f06f73cf6d487d75f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9d0e698b54e331467bf6c2842ea2ac.png)
您最近一年使用:0次
2023·全国·模拟预测
名校
7 . 如图1所示,四边形ABCD中
,
,
,
,
,M为AD的中点,N为BC上一点,且
.现将四边形ABNM沿MN翻折,使得AB与EF重合,得到如图2所示的几何体MDCNFE,其中
.
(1)证明:
平面FND;
(2)若P为FC的中点,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7605ce6f221ce8cad191da0f84a216d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2dcb2121af2b6d4ead458972439308.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/2f54442b-3ded-4f7d-a1d3-cfa199fb6ee6.png?resizew=344)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
(2)若P为FC的中点,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a3e7730e98d2af874d11664a5d084b.png)
您最近一年使用:0次
2023-11-22更新
|
1340次组卷
|
10卷引用:福建省漳州市诏安县桥东中学(霞葛教学点)2024届高三上学期第二次月考数学试题
福建省漳州市诏安县桥东中学(霞葛教学点)2024届高三上学期第二次月考数学试题(已下线)2024年普通高等学校招生全国统一考试理科数学领航卷(六)(已下线)2024年普通高等学校招生全国统一考试·信息卷理科数学(一)(已下线)2024年普通高等学校招生全国统一考试数学领航卷(八)(已下线)考点12 空间角 2024届高考数学考点总动员【练】宁夏石嘴山市平罗中学2023-2024学年高二上学期第三次月考数学试题(尖子班)吉林省辽源市田家炳高级中学校2023-2024学年高二上学期12月月考数学试题四川省成都市武侯高级中学2023-2024学年高二上学期12月月考数学试题青海省西宁市2024届高三上学期期末联考数学(理)试题(已下线)专题15 立体几何解答题全归类(9大核心考点)(讲义)-1
名校
8 . 如图,在四棱锥
中,底面
是菱形,
,平面
平面
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/39bd5a0c-1527-4eb3-bd64-a0d8a1f1c53a.png?resizew=170)
(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/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e1f990cb1de9609286fcd82d14cdf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/39bd5a0c-1527-4eb3-bd64-a0d8a1f1c53a.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e245440d3761fb4217eaa8dc303fa288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2023-11-19更新
|
350次组卷
|
3卷引用:福建省莆田五中、莆田八中、莆田十中、莆田侨中2023-2024学年高二上学期期末联考数学试卷
名校
解题方法
9 . 如图,正方体
的棱长为1,线段
上有两个动点E,F,且
,则下列结论中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e438a162ed349f7f25333e8f6c044e6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/868a0872-98b3-4366-8831-0617ac11ff39.png?resizew=163)
A.当E点运动时,![]() |
B.当E向![]() ![]() |
C.二面角![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
名校
10 . 如图,四边形ABCD是平行四边形,且
,四边形
是矩形,平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/1aac6c4f-9bfa-46b8-898f-af69fbc3db75.png?resizew=170)
(1)求证:
平面
;
(2)求平面
与平面
所成夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e35225f4d153a40ff5a6485590805a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a4e3f0349fa83dc2a0b7d798f04843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22437a2a3402609bfd4054a9f2b6c685.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/1aac6c4f-9bfa-46b8-898f-af69fbc3db75.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6541c0cb89f08aa4c937c0beb915e0a7.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
2023-11-15更新
|
696次组卷
|
4卷引用:福建省三明市第一中学2023-2024学年高二上学期12月月考数学试题