名校
解题方法
1 . 如图,
中,
,
是正方形,平面
平面
,若
、
分别是
、
的中点.
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6321a96e7f0768394f6932a121adc84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5352d28609d1b3d09a0a29d023d1bb72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf60ad9db3411f35704fa88d86bfef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2023-05-31更新
|
4847次组卷
|
14卷引用:甘肃省兰州市第二中学2021-2022学年高一下学期期末数学试题
甘肃省兰州市第二中学2021-2022学年高一下学期期末数学试题(已下线)模块一 专题5 立体几何初步(3)(北师大版)(已下线)模块一 专题5 立体几何初步(3)(人教B)(已下线)模块一 专题3 立体几何初步(3)(人教A)(已下线)第07讲 立体几何大题(11个必刷考点)-《考点·题型·密卷》(已下线)高一下学期期末数学考试模拟卷05-期中期末考点大串讲(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(2)江苏省常州市第一中学2022-2023学年高一下学期6月期末数学试题(已下线)模块一 专题5 立体几何初步(3)(苏教版)广西南宁市隆安县隆安中学2022-2023学年高一下学期数学期末复习预测试题辽宁省重点高中沈阳市郊联体2022-2023学年高一下学期期末数学考试试题辽宁省沈阳市辽中区第二高级中学2022-2023学年高一下学期期末考试数学试题黑龙江省齐齐哈尔市朝鲜族学校2022-2023学年高一下学期期末数学试题(已下线)第八章立体几何初步(单元测试)-【上好课】-(人教A版2019必修第二册)
2 . 如图1所示,在平面多边形
中,四边形
为长方形,
为正三角形,
,
,沿
将
折起到
的位置,使得平面
平面
(图2).
![](https://img.xkw.com/dksih/QBM/2022/10/18/3090189744463872/3094048473079808/STEM/a783d4ac1d404786ab84dd5f1e7b4930.png?resizew=423)
(1)证明:
;
(2)若点
为线段
的中点,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28c0e74a2053dc5ad9988154a7e1977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9db15366bd28ad77da8c1f300d8625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce552d6e4e8bca4d93e5cb01d8685600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0605f0eab4ccf706d8a82f7f86092c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9db15366bd28ad77da8c1f300d8625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987b90f5a645cb56a8db95dc3a7c38d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26bcf15939ea6ef6334e199640523cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/10/18/3090189744463872/3094048473079808/STEM/a783d4ac1d404786ab84dd5f1e7b4930.png?resizew=423)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fe20370c994eda681d4b73db18c4f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2ed2b90e45a160e26c5b6ee9d4fef8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
3 . 如图,四棱锥
中,四边形ABCD为梯形,其中
,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/0d16379a-a8de-46cb-991a-f0f41e873302.png?resizew=174)
(1)证明:
;
(2)若
,且PA与平面ABCD所成角的正弦值为
,点F在线段PC上满足
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca15fe5faca08d49a0382bc1941a497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d469943ad8454d37c58288b372b77c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e8433f8c8a712e6db0b639f326c420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/0d16379a-a8de-46cb-991a-f0f41e873302.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d3d65aec5acf9abc71a0a7f93e4f45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5339e9479014ef5df6cb7a43069a795e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4231eb3a564f1132b5543c18d58d5864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4655536451328bc4d8145b37376123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b0f49a7e2566e479f388aa67f9c4b2.png)
您最近一年使用:0次
2022-10-20更新
|
689次组卷
|
6卷引用:甘肃白银市第二中学2022-2023学年高三上学期一月月考理科数学试题
名校
4 . 如图,在四棱锥
中,底面ABCD为平行四边形,
,
,
,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/57d4f9e4-a876-4756-9dd5-3ff2ef0e5f7a.png?resizew=220)
(1)证明:
;
(2)若
,点E为棱AD的中点,求直线PE与平面PAB所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/57d4f9e4-a876-4756-9dd5-3ff2ef0e5f7a.png?resizew=220)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8254b52b379a420c17d38334940b073.png)
您最近一年使用:0次
2022-07-03更新
|
742次组卷
|
5卷引用:甘肃省庆阳市宁县第二中学2022-2023学年高三上学期11月月考数学试题
甘肃省庆阳市宁县第二中学2022-2023学年高三上学期11月月考数学试题河南省新乡市封丘县第一中学2021-2022学年高二下学期期末数学理科试题(已下线)专题1.4 空间向量的应用(4类必考点)山西大学附属中学校2022-2023学年高三上学期11月期中考试数学试题(已下线)9.5 空间向量与立体几何
解题方法
5 . 如图,在四棱锥
中,底面
为菱形,其中
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/02df2c0e-49da-4e03-b66c-713c148d8676.png?resizew=230)
(1)求证:
平面
;
(2)若平面
平面
,且
,求四棱锥
的体积.
![](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/931bbffda5e872703c9947eccc47ede2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/02df2c0e-49da-4e03-b66c-713c148d8676.png?resizew=230)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c51c4a1148587943fe9ba210f6141ee.png)
(2)若平面
![](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/a3261581eb9171dadfc3130d89c3e545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
您最近一年使用:0次
名校
解题方法
6 . 如图所示,已知平行四边形
和矩形
所在平面互相垂直,
,
,
,
,
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965909498707968/2966044149669888/STEM/2f78c2fda1814783aede3b7c85940ada.png?resizew=224)
(1)求证:
;
(2)设点
为一动点,若点
从
出发,沿棱按照
的路线运动到点
,求这一过程中形成的三棱锥
的体积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.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/ccc98c39f417673c1e9b6ab6f6c40ee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965909498707968/2966044149669888/STEM/2f78c2fda1814783aede3b7c85940ada.png?resizew=224)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b87b3be10408261827291574434d8e.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d0f06dc829e758727c532c608200f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d68be8df235af30390bc3d7b8195e2.png)
您最近一年使用:0次
2022-04-25更新
|
519次组卷
|
3卷引用:甘肃白银市第二中学2022-2023学年高三上学期一月月考文科数学试题
名校
解题方法
7 . 如图,在四棱锥P-ABCD中,平面
平面ABCD,
,
,
,
,
,E,H分别是棱AD,PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/24fc86d5-6fba-4427-ac37-44971b4cf24d.png?resizew=210)
(1)证明:
平面PCE;
(2)若
,求点P到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/24fc86d5-6fba-4427-ac37-44971b4cf24d.png?resizew=210)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b270ada8aaadf28043fa4525c57e653d.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥
中,面
平面ABCD,且底面ABCD是直角梯形,满足
,
,点G在线段PC上,且
.
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982748836143104/2985595570569216/STEM/63618391-f764-4144-b499-8eb722ab454e.png?resizew=284)
(1)求证:
;
(2)求证:PA
平面BDG.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4a812d0167e2c7b86caef15de703fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cf0ee918f8c2f753302d3b5928d358.png)
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982748836143104/2985595570569216/STEM/63618391-f764-4144-b499-8eb722ab454e.png?resizew=284)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90197a948331e61db644266368017e3.png)
(2)求证:PA
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
您最近一年使用:0次
2022-05-23更新
|
911次组卷
|
2卷引用:甘肃省兰州市第五十一中学2021-2022学年高一下学期期末考试数学试题
21-22高一·湖南·课后作业
名校
解题方法
9 . 如图,P是四边形ABCD所在平面外的一点,四边形ABCD是
的菱形,
,平面
垂直于底面ABCD,G为AD边的中点.求证:
平面PAD;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf65b8884909d735d575efe81a2d2ad.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
您最近一年使用:0次
2022-02-22更新
|
804次组卷
|
4卷引用:甘肃省高台县第一中学2021-2022学年高一下学期6月月考数学试题
甘肃省高台县第一中学2021-2022学年高一下学期6月月考数学试题(已下线)4.4.2 平面与平面垂直(已下线)第8章 立体几何初步(基础30题专练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)湘教版(2019)必修第二册课本习题4.4.2 平面与平面垂直
名校
解题方法
10 . 如图,在四棱锥P-ABCD中,四边形ABCD为菱形,PA=AB=2,PB=
,∠ABC=60°,且平面PAC⊥平面ABCD.
(2)若M是PC上一点,且BM⊥PC,求三棱锥M-BCD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(2)若M是PC上一点,且BM⊥PC,求三棱锥M-BCD的体积.
您最近一年使用:0次
2021-12-16更新
|
1192次组卷
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10卷引用:甘肃省张掖市某重点校2022-2023学年高三上学期第七次检测数学(文)试题
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