1 . 已知底面为菱形的四棱锥
中,
是等边三角形,平面
平面ABCD,E,F分别是棱PC,AB上的点,从下面①②③中选取两个作为条件,证明另一个成立;①F是AB的中点;②E是PC的中点;③
平面PFD.(只需选择一种组合进行解答即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137fcdac119eff6ac5990b6d201615df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/41200c40-477a-40d7-9dd6-132738e68091.png?resizew=201)
您最近一年使用:0次
解题方法
2 . 已知底面为菱形的四棱锥
中,
是等边三角形,平面
平面ABCD,E,F分别是棱PC,AB上的点.
![](https://img.xkw.com/dksih/QBM/2022/1/15/2894894675337216/2895916770123776/STEM/c41c7a00-3bcb-43c5-8498-57b0846541ec.png?resizew=224)
(1)从下面①②③中选取两个作为条件,证明另一个成立;
①F是AB的中点;②E是PC的中点;③
平面PFD.(只需选择一种组合进行解答即可)
(2)若
,
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://img.xkw.com/dksih/QBM/2022/1/15/2894894675337216/2895916770123776/STEM/c41c7a00-3bcb-43c5-8498-57b0846541ec.png?resizew=224)
(1)从下面①②③中选取两个作为条件,证明另一个成立;
①F是AB的中点;②E是PC的中点;③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137fcdac119eff6ac5990b6d201615df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec78c2154c5972efd438a6555afaf2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1112ffa328ed486ffc5e4a605eb510e.png)
您最近一年使用:0次
解题方法
3 . 如图,已知正方体
的棱长为1,E为
的中点,P为对角线上
的一个动点,过P作与平面ACE平行的平面,则此平面截正方体所得的截面( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/1205f59e-9d55-4904-923a-80e402aec6b5.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a46a98f42df8dd1d7ba89fe7e6961a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a7bcc1efb8a2ff57d64b6d057da463.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/1205f59e-9d55-4904-923a-80e402aec6b5.png?resizew=185)
A.截面不可能是五边形 |
B.截面可以是正六边形 |
C.P从D点向![]() |
D.截面面积的最大值为![]() |
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4 . 如图,已知三棱锥
中,
为
的中点,
为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2012/1/26/1570694447382528/1570694452838400/STEM/58751855bd734d72a1a6a4bca18ef4af.png?resizew=225)
(1)求证:
面
;
(2)找出三棱锥
中一组面与面垂直的位置关系,并给出证明(只需找到一组即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92569ef91dfcb7cd29c3636aac24b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2680fc712ba2729a5ebbeb6ff9633047.png)
![](https://img.xkw.com/dksih/QBM/2012/1/26/1570694447382528/1570694452838400/STEM/58751855bd734d72a1a6a4bca18ef4af.png?resizew=225)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)找出三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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5 . 如图,已知三棱锥
中,
,D为
中点,
为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2011/12/6/1570558621270016/1570558626742272/STEM/69794df487414bdab306d2c63120480b.png?resizew=217)
(I)求证:
面
;
(II)找出三棱锥
中一组面与面垂直的位置关系,并给出证明(只需找到一组即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036de574712cad14bddadf6653c7e714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2680fc712ba2729a5ebbeb6ff9633047.png)
![](https://img.xkw.com/dksih/QBM/2011/12/6/1570558621270016/1570558626742272/STEM/69794df487414bdab306d2c63120480b.png?resizew=217)
(I)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70364f7ba745daf15c2d638298503acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(II)找出三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
6 . 正方体
中,用平行于
的截面将正方体截成两部分,则所截得的两个几何体不可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.两个三棱柱 | B.两个四棱台 |
C.两个四棱柱 | D.一个三棱柱和一个五棱柱 |
您最近一年使用:0次
7 . 2021年11月第四届中国国际进口博览会在上海举办,此届博览会共有58个国家和3个国际组织参加国际展,127个国家和地区的近3000家参展商参加企业展.各式各样的商品首次亮相上海,其中一商品的部分结构可近似看做一个多面体,如图所示.在多面体
中,底面
为直角梯形,
,侧面
为菱形,平面
平面
,M为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/b31a5b64-2567-48ea-9232-562d302305aa.png?resizew=138)
(1)若
上有一点N满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
,确定点N的位置并证明;
(2)若
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46891551c0cc4d32ed8f8007e43846b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/b31a5b64-2567-48ea-9232-562d302305aa.png?resizew=138)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/426ffde6bbf525078771378acc6f58d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2246c0e92e8cc344f636ea8f8f9037e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebce46aeb97373353179e5669365fa4a.png)
您最近一年使用:0次
解题方法
8 . 如图,在正方体
中,点P是线段
上的一个动点,有下列三个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/fd2fd0fc-07ac-4c7a-b5c0-d77316122b86.png?resizew=175)
①
平面
;
②
;
③若点P与B不重合,则平面
平面
.
其中所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/fd2fd0fc-07ac-4c7a-b5c0-d77316122b86.png?resizew=175)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24579dca7ff1542ae019fc36110dddbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee37319c34c99cf839332a54dbcc68.png)
③若点P与B不重合,则平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5aaa754b644e971a79471566f75854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36bfdb78c3a35e0b79bf59e5f6a170b3.png)
其中所有正确结论的序号是( )
A.①②③ | B.②③ | C.①③ | D.①② |
您最近一年使用:0次