1 . 如图,在四面体
中,
、
分别是
、
的中点,
、
分别是
和
上的动点,且
与
相交于点
.下列判断中:
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498164163747840/2500042567884800/STEM/e48999ab93354a97a487cabcb5059cfd.png?resizew=328)
①直线
经过点
;
②
;
③
、
、
、
四点共面,且该平面把四面体
的体积分为相等的两部分.
所有正确的序号为
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498164163747840/2500042567884800/STEM/e48999ab93354a97a487cabcb5059cfd.png?resizew=328)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c6af53069897ada75e91c431645860.png)
③
![](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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
所有正确的序号为
您最近一年使用:0次
名校
解题方法
2 . 在四棱锥
中,
底面
,底面
为正方形,
,点
为正方形
内部的一点,且
,则直线
与
所成角的余弦值的取值范围为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91708c4508371f08556e76e31c7cb9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ddb2b4ebda1e8edf3ce24900505a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 如图所示,平面![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/5859c075bcc94e22bcae3481964360ea.png)
平面
,且四边形
为矩形,四边形
为直角梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/e9bc455f-7bd5-4021-ae9f-e8a6ee4b81b0.png?resizew=166)
(1)求证:
平面
;
(2)求平面
与平面
所成锐二面角的余弦值;
(3)求直线
与平面
所成角的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/5859c075bcc94e22bcae3481964360ea.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/7032f504a0794f1eac53a741f4304ae5.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/a0b7af46cb504388a730638590035ef5.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/5859c075bcc94e22bcae3481964360ea.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/a063c64e629a4cab89808ceeaf3c673c.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/2632e9e1befa41f29b5efab6b81a2105.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/b86d37b07e674f3aa5f693305c9c7f38.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/53a0a1cc143444a69b09f309cd6119ff.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/de5366bbde064a79837357316b198b8d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/e9bc455f-7bd5-4021-ae9f-e8a6ee4b81b0.png?resizew=166)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/4a93e89c83d647188c7cdd4c89db2c08.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/f8151008635d43c39f05a42914536c12.png)
(2)求平面
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/07d9bdf35d58436ea5c5c84da115619d.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/b83a7baa8b11473d8f76bdfd8d720132.png)
(3)求直线
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/7db11619fe08422bb9317e87c3d990da.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363347968/STEM/07d9bdf35d58436ea5c5c84da115619d.png)
您最近一年使用:0次