解题方法
1 . 如图,直线
和直线
均垂直于平面
,且
,
,
为线段
上一动点.
![](https://img.xkw.com/dksih/QBM/2024/1/16/3412361497305088/3412491456462848/STEM/dcf031b5178e44099345b5a54a29929a.png?resizew=131)
(1)求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
平面
;
(2)求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f6923bc38131265bed394a3b38937e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/2024/1/16/3412361497305088/3412491456462848/STEM/dcf031b5178e44099345b5a54a29929a.png?resizew=131)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
您最近一年使用:0次
名校
2 . 已知l,m,n是三条不同的直线,α,β,γ是三个不同的平面,则下列命题中正确的为( )
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-12-30更新
|
1145次组卷
|
7卷引用:广东省2024届高三第一次学业水平考试(小高考)数学模拟试题(三)
解题方法
3 . 如图,四棱锥
的底面ABCD是边长为2的正方形,E,F,M分别为边PD,PB,PC的中点,N为BF的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016855056179200/3018332359467008/STEM/d6b72fb7e8754bbd82724c1f3d4aeee5.png?resizew=159)
(1)证明:
平面AEF;
(2)若
,
,直线PA与平面ABCD所成的角为60°,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016855056179200/3018332359467008/STEM/d6b72fb7e8754bbd82724c1f3d4aeee5.png?resizew=159)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaa5e336f830a3e5cd60ff7a756f3ef.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5753a5af8f527fdb0f6a53f6ace72ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e313457381c401e884ca5880773992.png)
您最近一年使用:0次
2022-07-08更新
|
666次组卷
|
3卷引用:广东省2024年普通高中学业水平合格性考试考前冲刺数学试题三
广东省2024年普通高中学业水平合格性考试考前冲刺数学试题三广东省肇庆市2021-2022学年高一下学期期末数学试题(已下线)第12讲 8.6.2直线与平面垂直的判定定理(第1课时)-【帮课堂】(人教A版2019必修第二册)
解题方法
4 . 如图,在正方体
中,
是
的中点,
,
,
分别是
,
,
的中点,求证:
![](https://img.xkw.com/dksih/QBM/2022/5/8/2974933547376640/2979080373813248/STEM/e0efe439-5142-4d5a-b7ac-d28a804ac5a0.png?resizew=200)
(1)直线
平面
;
(2)
为线段
上一点,且
,求证:
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/8/2974933547376640/2979080373813248/STEM/e0efe439-5142-4d5a-b7ac-d28a804ac5a0.png?resizew=200)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31d54d125c042169e282f14eddd45a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f9d6c4583b60e2ece705889264f0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e82b3e225741b7f541fb6cff225d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
2022-05-14更新
|
1496次组卷
|
6卷引用:广东省2024年普通高中学业水平合格性考试考前冲刺数学试题二
广东省2024年普通高中学业水平合格性考试考前冲刺数学试题二广东省惠州一中、珠海一中、中山纪念中学2021-2022学年高一下学期第二次段考数学试题广东省深圳实验学校2021-2022学年高一下学期期中数学试题(已下线)第11练 空间直线、平面的平行-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)(已下线)空间直线、平面的平行(已下线)专题08 空间直线与平面的平行问题(1)-期中期末考点大串讲
5 . 《算数书》是我国现存最早的系统性数学典籍,其中记载有求“困盖”的术:置如其周,令相乘也,又以高乘之,三十六成一,该术相当于给出了由圆锥的底面周长
与高
,计算其体积
的近似公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137abb653a2c06df337b9a502c1818d1.png)
,用该术可求得圆周率
的近似值.现用该术求得
的近似值,并计算得一个底面直径和母线长相等的圆锥的表面积的近似值为9,则该圆锥体积的近似值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137abb653a2c06df337b9a502c1818d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec50b978abc75239e3087d03f9ba6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
A.![]() | B.2![]() | C.3![]() | D.3 |
您最近一年使用:0次
2021-03-28更新
|
691次组卷
|
3卷引用:广东省2024年普通高中学业水平合格性考试考前冲刺数学试题二
11-12高一下·甘肃兰州·期末
名校
6 . 已知m,n是两条不同直线,
,
是两个不同平面.以下命题中正确命题的个数是
①m,n相交且都在平面
,
外,
,
,
,
,则
;②若
,
, 则
; ③若
,
,
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
①m,n相交且都在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c6d37467a5c995d71e49408503927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79018590293277ff2d76452a50ad2dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4ded3c4bc7a2212f2a0eb5f9753de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c6d37467a5c995d71e49408503927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4ded3c4bc7a2212f2a0eb5f9753de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2020-03-20更新
|
351次组卷
|
6卷引用:广东省2024年普通高中学业水平合格性考试考前冲刺数学试题三
7 . 如图,在四棱锥
中,底面
是正方形,
平面
,且
,点
为线段
的中点.
(1)求证:
平面
;
(2)求证:
平面
.
![](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/e3f6967901d6c855864df01e7bf7a15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2018/11/27/2084522361585664/2089014872555520/STEM/7efcb83d96084868b4f7476647f83482.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2018-04-09更新
|
1409次组卷
|
6卷引用:广东省2024年普通高中合格性学业水平考试数学模拟数学试题一