1 . 如图:直三棱柱
中,
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572630313705472/1572630319996928/STEM/c9c07dcbbc39452eaaa6c8149d8431e0.png)
(Ⅰ)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18aee446eff8e431e170fae90e4de7ce.png)
(Ⅱ)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b446884bf8f1afc609a9e681998e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ba708880f5eb782acbf2c961c2494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572630313705472/1572630319996928/STEM/c9c07dcbbc39452eaaa6c8149d8431e0.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18aee446eff8e431e170fae90e4de7ce.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343d2cc05bba3afc674d7c9628980282.png)
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2016-12-04更新
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2卷引用:2015-2016学年甘肃省天水市秦安二中高二上学期期末理科数学试卷
名校
2 . 如图,在四棱锥P—ABCD中,底面ABCD为平行四边形,∠ADC=45°,
AD=AC=1,O为AC的中点,PO⊥平面ABCD,PO=1,M为PD的中点.
(Ⅰ)证明:PB∥平面ACM;
(Ⅱ)设直线AM与平面ABCD所成的角为α,二面角M—AC—B的大小
为β,求sinα·cosβ的值.
AD=AC=1,O为AC的中点,PO⊥平面ABCD,PO=1,M为PD的中点.
(Ⅰ)证明:PB∥平面ACM;
(Ⅱ)设直线AM与平面ABCD所成的角为α,二面角M—AC—B的大小
为β,求sinα·cosβ的值.
![](https://img.xkw.com/dksih/QBM/2017/9/5/1767548750602240/1768212839612416/STEM/6a8af875c8e34e48b844f35f9bf7739b.png?resizew=168)
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2016-12-04更新
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2卷引用:2015-2016学年甘肃省嘉峪关市酒钢三中高一上学期期末数学试卷
3 . 如图,三棱柱
中,侧棱
底面
,底面三角形
是正三角形,
是
中点,则下列叙述正确的是
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572549923749888/1572549929828352/STEM/15af3bf963124030a3bddf2972dfc2d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb9aaf34294bd0ebeac2df1449819cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19434b67703318b18be7efee7be590bd.png)
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572549923749888/1572549929828352/STEM/ef3f2bc9aaa345c897f20d8879ef2036.png)
![](https://img.xkw.com/dksih/QBM/2016/3/21/1572549923749888/1572549929828352/STEM/ef3f2bc9aaa345c897f20d8879ef2036.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/2016/3/21/1572549923749888/1572549929828352/STEM/15af3bf963124030a3bddf2972dfc2d2.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
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5卷引用:甘肃省兰州市第一中学2017-2018学年高一上学期期末考试数学试题
4 . 如图,在正方体ABCD﹣A1B1C1D1中,E为DD1的中点.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526322720768/1572526328807424/STEM/4f1d1fc78ff14abe883191e3463c23e3.png)
(Ⅰ)证明:BD1∥平面AEC;
(Ⅱ)证明:平面AEC⊥平面BDD1.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526322720768/1572526328807424/STEM/4f1d1fc78ff14abe883191e3463c23e3.png)
(Ⅰ)证明:BD1∥平面AEC;
(Ⅱ)证明:平面AEC⊥平面BDD1.
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5 . 如图,多面体
中,
两两垂直,且
,
.
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/428c4d43dfea47be83522b427064a793.png)
(1)若点
在线段
上,且
,求证:
;
(2)求多面体
的体积.
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/5d49424641304360973598f237f08595.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/96b17ab801b9449b99e2a5f08c77bf44.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/254aa9284b5d494aa9455c13770771eb.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/3d73e6f24e6042bb8f5e72b82ef8dfa3.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/428c4d43dfea47be83522b427064a793.png)
(1)若点
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/e382c30bb6aa4c52baef0e9121650194.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/206d2d9c3c4141d9ad49dae5d13ae402.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/89653a46b99e4d18b6f76e8197c6256d.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/eb99191592d94367906c2fef807963c8.png)
(2)求多面体
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510239883264/STEM/5d49424641304360973598f237f08595.png)
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2016-12-04更新
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616次组卷
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2卷引用:2016届甘肃省天水市一中高三上学期期末文科数学试卷
6 . 已知在四棱锥P-ABCD中,底面ABCD是矩形,PA⊥平面ABCD,PA=AD=1,AB=2,E,F分别是AB,PD的中点.
![](https://img.xkw.com/dksih/QBM/2015/3/13/1572006288261120/1572006294315008/STEM/d970bafc7cc944c1837f716f14afe612.png)
(1)求证:AF∥平面PEC;
(2)求PC与平面ABCD所成的角的正切值;
(3)求二面角
的正切值.
![](https://img.xkw.com/dksih/QBM/2015/3/13/1572006288261120/1572006294315008/STEM/d970bafc7cc944c1837f716f14afe612.png)
(1)求证:AF∥平面PEC;
(2)求PC与平面ABCD所成的角的正切值;
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95aa4d72790b1ce86e05a0e648f1e59d.png)
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