1 . 如图,在四棱锥
中,
底面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/b7a61586-c415-4115-8707-95df97a3c98a.png?resizew=239)
(1)求证:
平面
;
(2)若点
在线段
上,且满足
,求直线
与平面
所成角的正弦值.
![](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/a1cb23cb7d9f22cfc31a6cd6fcb12e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26eba7e649fade39fd2d0b6ef4ac5ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/b7a61586-c415-4115-8707-95df97a3c98a.png?resizew=239)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e8c1551d814f36aa6773ff5986c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2 . 如图,在五面体
中,四边形
为矩形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/51aee570-96d5-4998-9b97-5509c7b6eb86.png?resizew=142)
(1)证明:
平面
;
(2)连接
,
,若二面角
的大小为120,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/51aee570-96d5-4998-9b97-5509c7b6eb86.png?resizew=142)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d65b5127ccd01345f8bca5d8a94bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8845b922127348b8119107874264305e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca839944d0ac5155e2d78c094899b789.png)
您最近一年使用:0次
2019-05-18更新
|
672次组卷
|
3卷引用:河南省周口市淮阳一中2019-2020学年高一上学期第二次月考数学试题
3 . 如图,在四棱锥
中,
底面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2019/1/29/2129125985869824/2129740024487936/STEM/74990b8ce7374eca90781db39c3d4781.png?resizew=330)
(1)求证:
平面
;
(2)若
为
的中点,求点
到平面
的距离.
![](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/a1cb23cb7d9f22cfc31a6cd6fcb12e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26eba7e649fade39fd2d0b6ef4ac5ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2019/1/29/2129125985869824/2129740024487936/STEM/74990b8ce7374eca90781db39c3d4781.png?resizew=330)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2019-01-30更新
|
530次组卷
|
3卷引用:【市级联考】河南省周口市2019届高三上学期期末调研考试数学文科试题
10-11高三上·江苏南京·期中
解题方法
4 . 如图所示,在直三棱柱
中,
,
,
,
,
是棱
的中点.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405d4e4b1755e82269bb95b1e1a44d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1192b3111a6dad01bba5227472bb4072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4237f6a1fc115bb790aa10704b7908c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a783c7c0d9ae283307609e0cf9f30150.png)
![](https://img.xkw.com/dksih/QBM/2012/6/7/1570882593759232/1570882599149568/STEM/266c01fb273949bda7069a9d3e9b885c.png)
您最近一年使用:0次
5 . 如图所示,在四棱锥
中,底面
是矩形,
平面
,
.过
的中点
作
于点
,连接
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/ec317199-3e9a-4111-9db8-b815b2dba378.png?resizew=154)
(Ⅰ)证明:
平面
;
(Ⅱ)若平面
与平面
所成的锐二面角的余弦值为
,求
的长.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8067cc458cf12887177487c3cfb9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7784be0caa2ffb58bbebf81fa127c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/ec317199-3e9a-4111-9db8-b815b2dba378.png?resizew=154)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(Ⅱ)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193b5b41994c2a4dfa5bb0bc984061cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
解题方法
6 . 如图,在直三棱柱
中,四边形
是边长为
的正方形,
为
上的一点,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/2ad62c8f-392e-4cfe-8940-3ac514fb368f.png?resizew=152)
(1)求证:
平面
;
(2)若
与平面
所成角为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771d3d476f8c64d4a38b8260569dca3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2340abb56da9c571b7f17bb21cabe010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/2ad62c8f-392e-4cfe-8940-3ac514fb368f.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2477c7e17e4dbf3056d1558087407590.png)
您最近一年使用:0次
2017-05-29更新
|
809次组卷
|
2卷引用:河南省周口市2018届高三上学期期末抽测调研 数学(文)试题
名校
解题方法
7 . 如图,在三棱柱
中,已知
,
,点
在底面
上的投影是线段
的中点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/8c67e2f9-f104-45cb-a802-20c6670fe650.png?resizew=213)
(1)证明:在侧棱
上存在一点
,使得
平面
,并求出
的长;
(2)求三棱柱
的侧面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c462dcc5fba8c0a19d8b69366e01ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/8c67e2f9-f104-45cb-a802-20c6670fe650.png?resizew=213)
(1)证明:在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7ea432599108b34a0ccaa0f2c75e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
2017-02-16更新
|
1088次组卷
|
5卷引用:【全国市级联考】河南省周口市2017-2018学年高二下学期期末考试数学(文)试题