如图,在四棱锥
中,底面
是矩形,点
在棱
上(异于点
,
),平面
与棱
交于点
.
![](https://img.xkw.com/dksih/QBM/2017/5/4/1679679802572800/1679883070554112/STEM/a0a47f2ba01a4175907c48175dcf2ffc.png?resizew=180)
(1)求证:
;
(2)若平面
平面
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2017/5/4/1679679802572800/1679883070554112/STEM/a0a47f2ba01a4175907c48175dcf2ffc.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3602ec4c8f5ac2737fa78c05708c869f.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac559a1a89bfb16e1c44cdd7ad2f2bbd.png)
2017·江苏·三模 查看更多[2]
更新时间:2017-05-04 19:53:46
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【推荐1】如图1,在四边形ABCD中,AD∥BC,BC=2AD,E,F分别为AD,BC的中点,AE=EF,
.将四边形ABFE沿EF折起,使平面ABFE⊥平面EFCD(如图2),G是BF的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/75bb7365-b3af-46ed-8056-d73ed6abab37.png?resizew=496)
(1)证明:AC⊥EG;
(2)在线段BC上是否存在一点H,使得DH∥平面ABFE?若存在,求
的值;若不存在,说明理由;
(3)求二面角D-AC-F的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da624a70c1e27068e25d8c376e31dd8f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/75bb7365-b3af-46ed-8056-d73ed6abab37.png?resizew=496)
(1)证明:AC⊥EG;
(2)在线段BC上是否存在一点H,使得DH∥平面ABFE?若存在,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43191c681f342fbae9d4687198b5c8e4.png)
(3)求二面角D-AC-F的大小.
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【推荐2】如图,在以
为顶点的多面体中,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa64539ca44d1385217b4897bef25cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b9b8e52cd788d3a72a6fe6ef20e5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ffb3de83dea6b246028d656483bebc.png)
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/396d0c71-e9bb-4f96-8f15-8f7f9cd03213.png?resizew=174)
(1)请在图中作出平面
,使得
且
,并说明理由;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63a98f5ed97655875ffb3f9eb413d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a22d6b860f06fe23618b0d3de6768fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa64539ca44d1385217b4897bef25cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b9b8e52cd788d3a72a6fe6ef20e5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ffb3de83dea6b246028d656483bebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ea9d92e5c258a50af1e461c7388894.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/396d0c71-e9bb-4f96-8f15-8f7f9cd03213.png?resizew=174)
(1)请在图中作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4c9403b0642d53d8068c63e7f67010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4686e3f93c6ad5b950d1fbb9d4133a93.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b87b3be10408261827291574434d8e.png)
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【推荐1】读一读,回答问题.
屏风是中国古代居室内重要的家具、装饰品,其形制、图案及文字均包含有大量的文化信息,既能表现文人雅士的高雅情趣,也包含了人们祈福迎祥的深刻内涵.经过不断的演变,屏风有防风、隔断、遮隐的用途,而且起到点级环境和美化空间的功效,所以经久不衰、流传至今,并衍生出多种表现形式.各式各样的屏风,凝聚着手工艺人富于创意的智慧和巧夺天工的技术. 其实,屏风除了它的使用价值和美学价值外,还藏有一些几何定理,需要用心去体会.你能用几何模型来描绘屏风,并分析出它里面藏有的几何定理吗?
屏风是中国古代居室内重要的家具、装饰品,其形制、图案及文字均包含有大量的文化信息,既能表现文人雅士的高雅情趣,也包含了人们祈福迎祥的深刻内涵.经过不断的演变,屏风有防风、隔断、遮隐的用途,而且起到点级环境和美化空间的功效,所以经久不衰、流传至今,并衍生出多种表现形式.各式各样的屏风,凝聚着手工艺人富于创意的智慧和巧夺天工的技术. 其实,屏风除了它的使用价值和美学价值外,还藏有一些几何定理,需要用心去体会.你能用几何模型来描绘屏风,并分析出它里面藏有的几何定理吗?
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【推荐2】地球自西向东自转,造成了太阳每天东升西落运动.因这种现象是地球自转造成的人的视觉效果,所以天文学上把这种运动称为太阳周日视运动,其实质是地球自转的一种反映.研究太阳周日视运动轨迹对分析地球气候、计算当地日出日落时间、理解昼夜长短变化现象、设计建筑物日照时长等有重要意义.太阳周日视运动轨迹与太阳直射地球点有关,也与观测者当地的纬度有关.下图为春分(或秋分)日北纬
某地(如我国哈尔滨、松原、鸡西等地区)的太阳周日视运动轨迹图,
为当地观测者位置,圆平面
是观测者所在的地平面.直线
为天轴,其垂直于太阳视运动轨迹所在圆平面
,且与直线
在同一圆面上.两直线
和
相交于点
,夹角
为
.太阳早上
从正东方
点的地平面升起,中午
处于天空最高点
,傍晩
从正西方
点处落入地平面.
与地平面
所成锐二面角的平面角为多少?
(2)若图上
点为下午
太阳所在位置,此时阳光入射当地地平面的角度(即直线
与地平面
的夹角)为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb3250cd61600582b098da51aa5003a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77227d4d2b4a96829fd5ae1dd7cad688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77227d4d2b4a96829fd5ae1dd7cad688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfae15ca5c9acb4f5caf8be51d0dee0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f59348d20a25e936a8c357912e0c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ff697129f2f7c4f28f4904ea7322f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f59348d20a25e936a8c357912e0c35.png)
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(2)若图上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3a3871bde981fc6860439d77e411c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb3250cd61600582b098da51aa5003a.png)
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