1 . 如图所示,在直角梯形BCEF中,
,A、D分别是BF、CE上的点,AD∥BC,且AB=DE=2AD=2AF=2,(如图1)将四边形ADEF沿AD折起,连结BE、BF、CE(如图2).
![](https://img.xkw.com/dksih/QBM/2021/7/25/2771789133799424/2772716222431232/STEM/e584b5d9-309b-424f-bf31-0568b109601d.png?resizew=469)
(1)求证:AC∥平面BEF;
(2)当EF⊥CF时,求异面直线BF与EC所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4bc8ae79524e8f6ede68f1c2fa3c7f1.png)
![](https://img.xkw.com/dksih/QBM/2021/7/25/2771789133799424/2772716222431232/STEM/e584b5d9-309b-424f-bf31-0568b109601d.png?resizew=469)
(1)求证:AC∥平面BEF;
(2)当EF⊥CF时,求异面直线BF与EC所成角的余弦值.
您最近一年使用:0次
2 . 如图,矩形
中,
,
,
在
边上,且
,将
沿
折到
的位置,使得平面
平面
.
(Ⅰ)求证:
;
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82773737609e65dea3c5c67099f1b10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68696b781af2609327222d22cb7bab3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b348d4333ecdfc3e3b1ba16dc312550d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ced76e1ee551955a877688618b1f4ad.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5a101bb92bd721e35acc7023154b44.png)
![](https://img.xkw.com/dksih/QBM/2017/4/18/1668561570709504/1668648730017792/STEM/cd7d6f1167504c9eb741ff615f56b857.png?resizew=149)
您最近一年使用:0次
2017-04-18更新
|
2056次组卷
|
5卷引用:2020届内蒙古呼和浩特市高三第一次质量普查调研考试理科数学
3 . 在如图的几何体中,平面
为正方形,平面
为等腰梯形,
∥
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572207496101888/1572207502032896/STEM/e0524f40220c4161aef51aa302c112c4.png?resizew=196)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5181b97a7e43959b8455680157c3b644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4e574c9d139615d991a168cfbf63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5867254f6e74a3e31237279cd481f6.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572207496101888/1572207502032896/STEM/e0524f40220c4161aef51aa302c112c4.png?resizew=196)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572207496101888/1572207502032896/STEM/be0eba0b91914b259ed2983835344503.png?resizew=43)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572207496101888/1572207502032896/STEM/a4b78d26c7d44040a7b22ad19e2304da.png?resizew=37)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572207496101888/1572207502032896/STEM/a176a5724dcd40f08f52b75f4b2b13ba.png?resizew=39)
您最近一年使用:0次
2016-12-03更新
|
1061次组卷
|
5卷引用:2014届内蒙古呼伦贝尔市高三高考模拟二理科数学试卷
(已下线)2014届内蒙古呼伦贝尔市高三高考模拟二理科数学试卷(已下线)2014届内蒙古呼市二中高三模拟考试二理科数学试卷江苏省南京市玄武高级中学2020届高三下学期最后一卷数学试题2014-2015学年浙江省温州市十校联合体高二下学期期末联考数学试卷(已下线)模块检测卷二(B卷 滚动提升检查)-2021年高考数学一轮复习单元滚动双测卷(新高考地区专用)
2014·河北衡水·一模
名校
4 . 如图,已知长方形
中,
,
为
的中点.将
沿
折起,使得平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/b7cca480-f742-4365-b0e7-d6bb45df58ac.png?resizew=392)
(1)求证:
;
(2)若点
是线段
上的一动点,问点E在何位置时,二面角
的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571665321623552/1571665327529984/STEM/cb120fddf0834670a2402af1dec613f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1e88b36ff71fe69c07bade0f95f1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb5012f6c70a1e98d682b6d021fadd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/b7cca480-f742-4365-b0e7-d6bb45df58ac.png?resizew=392)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571665321623552/1571665327529984/STEM/166eea3c675d40da9df21ecb506066b3.png)
(2)若点
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571665321623552/1571665327529984/STEM/03d6e6e1eaaa4385828c1eb274fde031.png)
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571665321623552/1571665327529984/STEM/7d591459a7ff4a5b84f8bb101313da35.png)
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571665321623552/1571665327529984/STEM/4a0c98ebb87e4e59bece718a6f23563d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
您最近一年使用:0次
2016-12-03更新
|
2189次组卷
|
3卷引用:内蒙古包钢第一中学2015届高三适应性考试(一)数学(理)试题
5 . 如图,已知正三棱柱
的各棱长均相等,
是
的中点,点
在侧棱
上,且![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/47d454e830934277b353de36893b0242.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/7afbc56ba43044de9c16f9d0b220fca6.png)
(Ⅰ)求证:
⊥
;
(Ⅱ)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/32c59a107d064622bdc0529af952f9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/2c9f9de7d04a498e964fec41033b5240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/fb84216941e041568d196d3e262f533b.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/47d454e830934277b353de36893b0242.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/7afbc56ba43044de9c16f9d0b220fca6.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/2c7ac55d36414b2cae054036bbfaa63a.png)
(Ⅱ)求二面角
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572127128469504/1572127134572544/STEM/1d895c6918a7488bbfa87101d0705a6d.png)
您最近一年使用:0次
6 . 如图所示,矩形ABCD中,AD⊥平面ABE,AE=EB=BC=2,
F为CE上的点,且BF⊥平面ACE
(1)求证:AE⊥平面BCE;
(2)求证:AE∥平面BFD;
F为CE上的点,且BF⊥平面ACE
(1)求证:AE⊥平面BCE;
(2)求证:AE∥平面BFD;
![](https://img.xkw.com/dksih/QBM/2012/2/22/1570764162613248/1570764167774208/STEM/13fd70e31b4b4f45b732f9c563c83ac7.png)
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