名校
解题方法
1 . 如图,已知正方体
,点
、
、
分别为棱
、
、
的中点,下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.![]() ![]() | B.平面![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2024-03-03更新
|
1701次组卷
|
8卷引用:安徽省黄山市2024届高中毕业班第一次质量检测数学试题
安徽省黄山市2024届高中毕业班第一次质量检测数学试题(已下线)专题19 平面与平面平行-《重难点题型·高分突破》(人教A版2019必修第二册)吉林省白城市洮南市第一中学2023-2024学年高一下学期4月阶段性考试数学试题河南省新乡市封丘县第一中学2023-2024学年高一下学期4月阶段性考试数学试题(已下线)高一下学期第三次月考模拟卷(新题型)--同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)专题13.5空间平面与平面的位置关系-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)专题3.5空间直线、平面的平行-重难点突破及混淆易错规避(人教A版2019必修第二册)云南省昆明市云南师范大学附属中学2023-2024学年高一下学期教学测评月考(七)数学试题
解题方法
2 . 如图,四棱锥
,其中
为正方形,
底面
,
,
,
分别为
,
的中点,
,
在棱
,
上,且满足
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/7ed4a1cf-1830-4c24-9e70-82b9d0bce50d.png?resizew=152)
(1)求证:直线
与直线
相交;
(2)求平面
与平面
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0cf7a89ea148e0481a56f127297bb2.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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b52e2c90e1d9fc17415aeef9a574bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15120d7841b36be2453a05a9447d0de5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/7ed4a1cf-1830-4c24-9e70-82b9d0bce50d.png?resizew=152)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360496a4f5cc8a5faca5e089ae4f9531.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8be7470f11eed5536f3baf65e3a125d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-05-10更新
|
434次组卷
|
2卷引用:安徽省芜湖市2023届高三下学期5月教学质量统测数学试题
3 . 在如图所示的多面体
中,面
是边长为
的菱形,
,
,
面
,
,且
.
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572584036032512/1572584041889792/STEM/4c0e1539c1fb422bbf2ba816d067bea9.png)
(I)证明:
平面
;
(II)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e38a1b5cfffd43a3405481a1d67cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c4c9080c1a87ece36994d63fea3131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90fb211f34523ab8b8809c2b9efb8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f11e5b3ebac5f333e53ba46fb88f7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e744a2d5ee025ce599d7241dcbba89fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4fcd27e5eacfa328372b6b0e41538f.png)
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572584036032512/1572584041889792/STEM/4c0e1539c1fb422bbf2ba816d067bea9.png)
(I)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8badfeb9e7556486e02ab60df4dd32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(II)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffee8b7eff437080a0936d837ceabe95.png)
您最近一年使用:0次
4 . 如图,在四棱锥
中,底面
是直角梯形,侧棱
底面
,
垂直于
和
,
,
.
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572579137347584/1572579143229440/STEM/36eea8c2257a4d26beb0e373afb9ce0e.png)
(1)求证:
平面
;
(2)求平面
与平面
所成的二面角的余弦值;
(3)设点
是直线
上的动点,
与平面
所成的角为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20dc940044210101ae8bbb17b37120c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b0c4c783dd55685bd3e88bb31c6696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f5457bbeaaf4d6da96fc3ed2c6e61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b0c4c783dd55685bd3e88bb31c6696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d86a0a3e867a448094f74a54a1fee64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b693717f525facc79b9a500ed998b109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588a2119bc5e8cdf4731828b195a7892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f017bdeb820f8d9c6cd4ab5c8d678b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb1ae276659258455e7b41088b706e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9c827e46d1a395fafbf15cdd6c6c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8c67c8343701a69505477827538f72.png)
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572579137347584/1572579143229440/STEM/36eea8c2257a4d26beb0e373afb9ce0e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cfb3721d007a9fcbc86a3919a11f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dd7a72d80ec9bb5db3e1537c291e97.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dd7a72d80ec9bb5db3e1537c291e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a14f2edcb16e66233e4ec720377d25.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f92c0005348ac35069a9fd56068da81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a44be92f38e063a01b8cd67418815cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09617a717b8f018f295fd517a0c3f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a14f2edcb16e66233e4ec720377d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ab55147ca5c0f958af43b0637ee31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee27e22d0fbd0497a1555556df747456.png)
您最近一年使用:0次
5 . 如图,PDCE为矩形,ABCD为梯形,平面PDCE⊥平面ABCD,∠BAD=∠ADC=90°,AB=AD=
CD=1,PD=
.
![](https://img.xkw.com/dksih/QBM/2014/7/8/1571816802746368/1571816808677376/STEM/ff8eaccef82a491a9655c177f2410bbd.png)
(1)若M为PA中点,求证:AC∥平面MDE;
(2)求直线PA与平面PBC所成角的正弦值;
(3)在线段PC上是否存在一点Q(除去端点),使得平面QAD与平面PBC所成锐二面角的大小为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2014/7/8/1571816802746368/1571816808677376/STEM/ff8eaccef82a491a9655c177f2410bbd.png)
(1)若M为PA中点,求证:AC∥平面MDE;
(2)求直线PA与平面PBC所成角的正弦值;
(3)在线段PC上是否存在一点Q(除去端点),使得平面QAD与平面PBC所成锐二面角的大小为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdab625e32e38d1c72c901cece0e147.png)
您最近一年使用:0次