1 . 如图,在四棱锥
中,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/bd29c939e1e949ed8766f2ab3468e016.png)
(1)若
为
的中点,求证:
平面
;
(2)求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/eeda0ca9975a4f69bf1ed51303d74b82.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/60aa0e7fb4e5426a83018f59dcfee2a4.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/b072b81a583c49b8a40369c1dab647bb.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/0f9a8dbd01a047d5bfc946d3b7ec5286.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/9ca9dc11dedd427884fcf5e96ce70dbe.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/bd29c939e1e949ed8766f2ab3468e016.png)
(1)若
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/a1b9d491ce574191ad80ea24f960f4db.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/4e68dc11a7a94a3ebccbc3378b6b8849.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/dd1bc81645f54fe1834c777605744191.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/a022b6b5af0848f68c6b739e7aacbd51.png)
(2)求三棱锥
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037695066112/1573037701095424/STEM/da82a1e462ae4d40a38b9b36544bcdd3.png)
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2016-12-04更新
|
553次组卷
|
3卷引用:2015-2016学年云南玉溪一中高二下期中文科数学试卷
2 . 在棱长为2的正方体
中,设
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/9819ab4b8be54c81978cbe724e09f2d8.png)
(1)求证:
;
(2)求证:
平面
;
(3)求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/71bb2842ec724f50b21e4be6fa1fd05d.png)
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/5ce0237a91d2464dabdc86c3daa68fc9.png)
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/42aacbac34f346c19d7823bf37a4b2d2.png)
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/9819ab4b8be54c81978cbe724e09f2d8.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/d428ba809c24429f95de5decfc42a707.png)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/511c51fb488446ce80a821d15aa70d74.png)
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/5a761779045847c78e6df18fb685dd2c.png)
(3)求三棱锥
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572475946565632/1572475952553984/STEM/38384b4a31ec4451b3dcedcdccec34ab.png)
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3 . 如图,四边形
为菱形,
,
平面
,
为
中点.
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/25022f7b071142949ffb650a622a7cb2.png)
(Ⅰ)求证:平面![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/dd065e0c588c422c9c2e7fb797ff4d3a.png)
平面
;
(Ⅱ)若
,求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/3448deab3c1c4bb4a42b670ef6ea9937.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/1f9d7da21b674db593dcaefecc080f93.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/4a3d5727b3d84ee2baf184a61ee459d5.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/3448deab3c1c4bb4a42b670ef6ea9937.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/b2000586f4d24486878d52ae2a518a27.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/6ec667666e7e4acf82e1d3f421885963.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/25022f7b071142949ffb650a622a7cb2.png)
(Ⅰ)求证:平面
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/dd065e0c588c422c9c2e7fb797ff4d3a.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/e4a97b203f7740b2ba1d9032bf5e7a9a.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/3448deab3c1c4bb4a42b670ef6ea9937.png)
(Ⅱ)若
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/89c0cf4bd3c04f18845414484b0c46fd.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572422198607872/1572422204768256/STEM/ed820304111645bbaf9b9315d2797bd1.png)
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