1 .
如图,四棱锥
的底面是矩形,
底面
,
为
边的中点,
与平面
所成的角为45°,且
.
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的余弦的大小.
如图,四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3cef288b1d0a515ec4c33b70dba9cc.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b74a32c8ccd8a3632c8d79e5eb51cc.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9881fe0907622c2e4f0d66c1011f4ce6.png)
您最近一年使用:0次
2 . 如图,在四棱锥P﹣ABCD中,底面ABCD是边长为
的正方形,E为PC的中点,PB=PD.
(1)证明:BD⊥平面PAC.
(2)若PA=PC=2,求三棱锥E﹣BCD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
(1)证明:BD⊥平面PAC.
(2)若PA=PC=2,求三棱锥E﹣BCD的体积.
![](https://img.xkw.com/dksih/QBM/2011/3/29/1570085169635328/1570085174771712/STEM/9a3cd1a85c474670885d69268cdfb59e.png?resizew=176)
您最近一年使用:0次
3 . 如图,在三棱锥
中,
是等边三角形,∠PAC=∠PBC=90º.
(1)证明:AB⊥PC;
(2)若
,且平面
⊥平面
,求三棱锥
体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
(1)证明:AB⊥PC;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eea78bf026d76f1cb9cc3dc9349a193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2016-11-30更新
|
1951次组卷
|
5卷引用:新疆维吾尔自治区乌鲁木齐市第一中学2023届高三第三次诊断性测试数学(文)试题