如图所示,在四棱锥P﹣ABCD中,PA⊥底面ABCD,且底面ABCD为正方形,E是PA的中点.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526206304256/1572526212177920/STEM/a20b1ce4165a4cdf85baad3acc2ee8dd.png)
(Ⅰ)求证:PC∥平面BDE;
(Ⅱ)求证:平面PAC⊥平面BDE.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526206304256/1572526212177920/STEM/a20b1ce4165a4cdf85baad3acc2ee8dd.png)
(Ⅰ)求证:PC∥平面BDE;
(Ⅱ)求证:平面PAC⊥平面BDE.
更新时间:2016-12-04 03:35:40
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解答题-问答题
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【推荐1】在梯形PBCD中,A是PB的中点,DC∥PB,DC⊥CB,且PB=2BC=2DC=4(如图1所示),将三角形PAD沿AD翻折,使PB=2(如图2所示),E是线段PD上的一点,且PE=2DE.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526206304256/1572526212276224/STEM/6999cf44daa6481e97d0877d363d1ec1.png)
(Ⅰ)求四棱锥P﹣ABCD的体积;
(Ⅱ)在线段AB上是否存在一点F,使AE∥平面PCF?若存在,请指出点F的位置并证明,若不存在请说明理由.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526206304256/1572526212276224/STEM/6999cf44daa6481e97d0877d363d1ec1.png)
(Ⅰ)求四棱锥P﹣ABCD的体积;
(Ⅱ)在线段AB上是否存在一点F,使AE∥平面PCF?若存在,请指出点F的位置并证明,若不存在请说明理由.
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解题方法
【推荐2】如图,在矩形
中,
,
为
的中点.将
沿
折起,使得平面
平面
.点
是线段
的中点.
(Ⅰ)求证:平面
平面
;
(Ⅱ)求证:
;
(Ⅲ)过
点是否存在一条直线
,同时满足以下两个条件:
①
平面
;②
.
请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b11c2fdc1313cbe590ef666ad27ccb7.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e7fa0fe4077f21e444ce846e6827b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4254f64ccfb853160337ac9cce797c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4703beacb3c3d5fcb9009f9d59df5dd8.png)
(Ⅲ)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673966d67224d888647f8c1b2e5ca461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e1b1c21b9eda40498edd1c3173af503.png)
请说明理由.
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572125410082816/1572125415956480/STEM/47d6d88ec6ef4d159278c22dad9c45d3.png)
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【推荐1】如图,在直三棱柱
中,
,
,
,
,M是棱
的中点,
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;
求直线AM与平面
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/99e33b60-42e3-4e15-8672-35f184102c53.png?resizew=145)
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【推荐2】如图所示,平面多边形
中,AE=ED,AB=BD,且
,现沿直线
,将
折起,得到四棱锥
.
![](https://img.xkw.com/dksih/QBM/2018/2/28/1891898824294400/1910512682786816/STEM/62a6b5431f2b44f39341d9d5836f0f9e.png?resizew=294)
(1)求证:
;
(2)若
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所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6723f8b9d907981aa735cd96386bee36.png)
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