名校
1 . 如图,空间六面体
中,
,
,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
平面
为正方形,平面
平面
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
;
(2)若
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec123fb520885455b57bf7613e1b9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa32bd49a6554a2722444d71315920f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdffc89ee1fe3e56de89222ad3313cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0b950951cf1ebf3f04b77ca00301e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecad5f4090684e0c60fb228a2ba471c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378c9b0145b88657c2536e43d27123fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-04-10更新
|
460次组卷
|
2卷引用:甘肃省2024届高三下学期3月月考(一模)数学试题
名校
2 . 如图,在四面体
中,
平面
是
的中点,
是
的中点,点
满足
.
(1)证明:
平面
;
(2)若
与平面
所成的角大小为
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999c8f0e34d080fbbc53f97e5317bbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91f0750166d53342ab1db4f85dee0f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/acb00f66-5b21-4743-843c-eed0ccffedfd.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-11-11更新
|
211次组卷
|
2卷引用:甘肃省兰州市第六十一中学(兰化一中)2024届高三上学期期末数学试题
名校
3 . 如图,在几何体
中,平面
平面
,四边形
为菱形,
,
,
,M为
中点.
![](https://img.xkw.com/dksih/QBM/2020/10/9/2567400978063360/2574473828024321/STEM/bc20c422a8044863ad9c4e5393c131e3.png?resizew=202)
(1)求证:
平面
;
(2)求平面
与平面
所成二面角(不大于90°)的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.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/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90101de7db431b9632452fb694622379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41d3f7d55fcbaebc4e2450ac63a3dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2020/10/9/2567400978063360/2574473828024321/STEM/bc20c422a8044863ad9c4e5393c131e3.png?resizew=202)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39284c1ef4a749b8683a7c79c4246672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
您最近一年使用:0次
4 . 如图,四棱锥
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/c12a25b8-e708-4c29-b803-9dca076d8c5f.png?resizew=155)
求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b577ea0e75873c8a27aaa3ed615d1f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/c12a25b8-e708-4c29-b803-9dca076d8c5f.png?resizew=155)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2017-12-03更新
|
1373次组卷
|
4卷引用:甘肃省定西市岷县二中2017-2018学年高二下学期期中考试数学(文)试题
名校
5 . 如图,在四棱锥
中,底面
是菱形,
为
的中点,
为
的中点.证明:直线
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
您最近一年使用:0次
2017-12-03更新
|
961次组卷
|
7卷引用:【全国百强校】甘肃省兰州第一中学2018-2019学年高一12月月考数学试题