名校
1 . 如图,
是边长为
的菱形,
,
平面
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/574dd9da-9c6d-4bd7-8673-f6f5680638ce.png?resizew=174)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477dc280b77f5640565dbc0ddf24460a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36f7e5128bcf12583792fe8a4a4d8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa764f3aa7ae96d581733661f7e78c23.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/574dd9da-9c6d-4bd7-8673-f6f5680638ce.png?resizew=174)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de4a54cc7818be87a239f6de5f5d05b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
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3卷引用:甘肃省兰州市2018届高三第二次实战考试理科数学
2 . 在四棱锥
中, 底面
为平行四边形,
点在底面
内的射影
在 线段
上, 且
为
的中点,
在线段
上, 且
.
![](https://img.xkw.com/dksih/QBM/2017/4/13/1664769990254592/1664858970628096/STEM/dd7eef7c-cde4-450e-b0b3-50aa4ccd6b3f.png?resizew=185)
(1) 当
时, 证明: 平面
平面 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de5641db7accfdb1aed4afc9c067ac1.png)
当平面
与平面
所成二面角的正弦值为
时, 求四棱锥
的体积.
![](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/6ef064b7768e77e3e8d32f3f96e453f2.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a584d9a1d45b7f8e0983e8ccab84bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/37b6e823d73097c0bf9a244c94ab4f08.png)
![](https://img.xkw.com/dksih/QBM/2017/4/13/1664769990254592/1664858970628096/STEM/dd7eef7c-cde4-450e-b0b3-50aa4ccd6b3f.png?resizew=185)
(1) 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6742cc605e3d1fa702b3479b28606131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de5641db7accfdb1aed4afc9c067ac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd23eefdd44e679b004f2c978e87208e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec53c9cc69c2e3943ec8df5d5b5d44c7.png)
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4卷引用:甘肃省兰州第一中学2017届高三冲刺模拟考试数学(理)试题
甘肃省兰州第一中学2017届高三冲刺模拟考试数学(理)试题2016-2017学年河北省唐山市高三年级第二次模拟考试理科数学试卷四川省双流中学2018届高三11月月考数学(理)试题(已下线)专题19 几何体的表面积与体积问题——备战2022年高考数学二轮复习常考点专题突破
3 . 如图所示的空间几何体
中,四边形
是边长为2的正方形,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2017/4/11/1663341618724864/1663558947717120/STEM/0c29e4864e3a4bb9b680c9cb753c2a95.png?resizew=191)
(1)求证:平面
平面
;
(2)求平面
与平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e38a1b5cfffd43a3405481a1d67cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f36d315245b63a811d5c6f348c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc143c7fd7c471ca91b6ccc22438fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5602f77ca3a869d3898320643005a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86338536656046e93b53672ade9a78b3.png)
![](https://img.xkw.com/dksih/QBM/2017/4/11/1663341618724864/1663558947717120/STEM/0c29e4864e3a4bb9b680c9cb753c2a95.png?resizew=191)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f5c2097f668c484d698d7f59c237ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d666dd3308604685e59f4ca22663b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
4 . 如图,四棱锥P−ABCD中,PA⊥底面ABCD,AD∥BC,AB=AD=AC=3,PA=BC=4,M为线段AD上一点,AM=2MD,N为PC的中点.
(Ⅱ)求直线AN与平面PMN所成角的正弦值.
(Ⅱ)求直线AN与平面PMN所成角的正弦值.
您最近一年使用:0次
2016-12-04更新
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74卷引用:甘肃省兰州市五十九中2022-2023学年高三下学期高考模拟考试数学(理科)试题
甘肃省兰州市五十九中2022-2023学年高三下学期高考模拟考试数学(理科)试题2016年全国普通高等学校招生统一考试理科数学(新课标3卷精编版)2017届山西大学附中高三二模测试数学试卷江西省横峰中学、铅山一中、德兴一中2018届高三上学期第一次月考数学(理)试题人教A版高中数学 高三二轮 专题05 立体几何中的空间角问题 测试(已下线)《考前20天终极攻略》5月26日 立体几何与空间向量【理科】【全国百强校】吉林省长春外国语学校2019届高三上学期期末考试数学(理)试题【全国百强校】吉林省长春市吉林省实验中学2019届高三上学期第三次月考数学(理科)试题上海市上海中学2017届高三上学期10月月考数学试题上海市格致中学2017届高三上学期10月月考数学试题广东省佛山市南海区2020届高三统一调研测试(一)数学试题湖南省八校2018-2019学年高三上学期暑期返校考试数学(理)试题甘肃省静宁县第一中学2020届高三第七次模拟考试数学(理)试题(已下线)专题17 立体几何综合-五年(2016-2020)高考数学(文)真题分项(已下线)专题17 立体几何综合-五年(2016-2020)高考数学(理)真题分项江苏省南京市金陵中学2020-2021学年高三上学期8月学情调研测试数学试题江苏省南京市秦淮中学2020-2021学年高三上学期10月月考数学试题(已下线)易错点10 立体几何中的角-备战2021年高考数学(理)一轮复习易错题重庆市第八中学校2021届高三上学期阶段性检测(3)数学试题(已下线)解密07 空间几何中的向量方法(讲义)-【高频考点解密】2021年新高考数学二轮复习讲义+分层训练西藏自治区山南市第三高级中学2021届高三第四次月考数学(文)试题西藏自治区山南市第三高级中学2021届高三第四次月考数学(理)试题江西省南昌市第三中学2021届高三下学期第八次月考试数学(理)试题浙江省杭州市桐庐中学2020-2021学年高三上学期暑期阶段性测试数学试题(已下线)专题08向量方法解决角和距离(练)(理科)第一篇 热点、难点突破篇-《2022年高考理科数学二轮复习讲练测》(全国课标版)(已下线)理科数学-2022年高考押题预测卷01(全国乙卷)上海实验学校2022届高三冲刺模拟4数学试题西藏自治区拉萨中学2022届高三下学期第八次月考数学(理)试题(已下线)专题17 立体几何解答题浙江省杭州市桐庐中学2022-2023学年新高三暑期阶段性测试数学试题2023届甘肃省高考数学模拟试卷(二)2023届甘肃省高考理科数学模拟试卷(四)上海市敬业中学2022届高三上学期10月月考数学试题(已下线)2016年全国普通高等学校招生统一考试理科数学(全国3卷参考版)(已下线)专题24 空间向量与空间角的计算-十年(2011-2020)高考真题数学分项福建省福州市鼓山中学2023届高三适应性练习数学试题福建省泉州市泉州鲤城北大培文学校2022届高三上学期期末数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点1 平面法向量求法及其应用(一)【基础版】(已下线)第32题 空间角求法迭出,向量法更胜一筹(优质好题一题多解)(已下线)6.3 空间中的平行关系与垂直关系(高考真题素材之十年高考)(已下线)6.4 空间向量与立体几何(高考真题素材之十年高考)1(已下线)6.4 空间向量与立体几何(高考真题素材之十年高考)1 (2)(已下线)专题23 立体几何解答题(理科)-1河北省邢台市第一中学2017-2018学年高二上学期第二次月考数学(文)试题福建省福州市闽侯第六中学2017-2018学年高二上学期期中考试数学(文)试题河北省临漳县第一中学2017-2018学年高二下学期第三次月考数学(理)试题浙江省湖州市菱湖中学2018-2019学年高二12月月考数学试题【全国百强校】黑龙江省牡丹江市第一高级中学2018-2019学年高二上学期期末考试数学(理)试题【全国百强校】陕西省西安市长安区第一中学2018-2019学年高二上学期期末考试数学(理)试题【全国百强校】贵州省铜仁市第一中学2018-2019学年高二下学期期中考试数学(理)试题湖北省黄冈市2019-2020学年高二上学期10月月考数学试题重庆市朝阳中学2019-2020学年高二上学期12月月考数学试题辽宁省盘锦市兴隆台区辽河油田第二高级中学2019-2020学年高二上学期期末数学试题青海省西宁市第十四中学2019-2020学年高二上学期期中数学(理)试题河北省张家口市第一中学2018-2019学年高一衔接班下学期期末数学试题河北省博野中学2019-2020学年高二上学期12月月考数学试题广东省茂名市电白区2018-2019学年高二下学期期末数学(理)试题(已下线)【新东方】绍兴高中数学00032重庆市第七中学2020-2021学年高二上学期期中数学试题湖北省武汉市光谷第二高级中学2020-2021学年高二下学期6月月考数学试题广东省惠州市第一中学2021-2022学年高二上学期第一次考试数学试题陕西省西安市长安区第一中学2021-2022学年高二上学期9月第一次质量检测理科数学试题湖南省长沙市雅礼中学2021-2022学年高二上学期9月月考数学试题河北省唐山市滦南县第一中学2021-2022学年高二上学期10月月考数学试题上海市大同中学2022-2023学年高二上学期10月月考数学试题海南省洋浦中学2022-2023学年高二上学期期中检测数学试题上海市进才中学2022-2023学年高二上学期10月月考数学试题【新教材精创】1.4.2+用空间向量研究距离、夹角问题(2)教学设计-人教A版高中数学选择性必修第一册【新教材精创】1.4.2+用空间向量研究距离、夹角问题(2)导学案-人教A版高中数学选择性必修第一册(已下线)广东省惠州市2017-2018学年高二上学期期末教学质量检测数学(理)试题浙江省嘉兴市桐乡市高级中学2022-2023学年高二上学期9月检测数学试题章末总结四川省南充市阆中市阆中中学校2023-2024学年高二上学期11月月考数学试题福建省莆田市仙游第一中学等五校联考2022-2023学年高二上学期期末数学试题
5 . 如图,在四棱锥
中,侧面
底面
,底面
为矩形,
,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/2016/6/22/1572786155315200/1572786161614848/STEM/b5dd853c830d487b9a2894ea70688690.png?resizew=221)
(1)求证:
;
(2)若
与平面
所成的角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce965313d0ebce23a3b66ea8366187fe.png)
![](https://img.xkw.com/dksih/QBM/2016/6/22/1572786155315200/1572786161614848/STEM/b5dd853c830d487b9a2894ea70688690.png?resizew=221)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b87a95accd0dcf9154737859bba2f1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a37874cd284fb1a8c864769ce50c9.png)
您最近一年使用:0次
2016-12-04更新
|
952次组卷
|
2卷引用:2016年甘肃省兰州市高三实战考试理科数学试卷
名校
6 . 如图,已知矩形
所在平面垂直于直角梯形
所在平面于直线
,且
,
且
∥
.
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572498107219968/1572498112643072/STEM/4b93084b204b4899a29cd8ac278ceab5.png?resizew=177)
(Ⅰ)设点
为棱
中点,求证:
平面
;
(Ⅱ)线段
上是否存在一点
,使得直线
与平面
所成角的正弦值等于
?若存在,试确定点
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1195c8aeabf1925d6980b8de505e4050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ee06b35a55efafdc6c9b4839195dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13eaa22726a8645009cede35eaba2f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572498107219968/1572498112643072/STEM/4b93084b204b4899a29cd8ac278ceab5.png?resizew=177)
(Ⅰ)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ee5f3950aa6f59c76cf91c3ed8f290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(Ⅱ)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2016-12-04更新
|
1681次组卷
|
8卷引用:甘肃省兰州大学附属中学2020-2021学年高三上学期12月月考数学理科试题
7 . 如图,在四棱柱
中,底面
是等腰梯形,
∥
,
,
,顶点
在底面
内的射影恰为点
.
![](https://img.xkw.com/dksih/QBM/2015/4/13/1572067092578304/1572067098574848/STEM/002190a486bb43d5ae43121d17d9bbd2.png)
(1)求证:
;
(2)若直线
与直线
所成的角为
,求平面
与平面
所成角(锐角)的
余弦函数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8456cee87c4e22351affc28f3a73a0f2.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2015/4/13/1572067092578304/1572067098574848/STEM/002190a486bb43d5ae43121d17d9bbd2.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c530ae8e3cc2e7055c7e1fb2996fac1d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdab625e32e38d1c72c901cece0e147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
余弦函数值.
您最近一年使用:0次
8 . 如图,在四边形
中,
,
,点
为线段
上的一点.现将
沿线段
翻折到
(点
与点
重合),使得平面![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/205e702acfa5443492e490de85abc712.png)
平面
,连接
,
.
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/15c6e3d42cac4525a600cfaa0bb56f3c.png)
(Ⅰ)证明:
平面
;
(Ⅱ)若
,且点
为线段
的中点,求二面角
的大小.
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/4e90e9a7d2d9485c81de1c28a371ec85.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/59f3d39d8b2942d499d96191962dcc15.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/2a9628a8e1654901b38a501b00dd71be.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/6450cd136387418c87e9d98aacdd2077.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/ac27ad21c2194557be480869af58a20e.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/9725de35452d4f87bb60e896079da649.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/bfc37f8d7557434fa8d97d9b630ff675.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/205e702acfa5443492e490de85abc712.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/f8414d9f81d74f8f948a19c507c92c30.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/f08139489694499285d2200294e31d74.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/205e702acfa5443492e490de85abc712.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/4ed2bc8cd8a94e3a879644272e063c1a.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/82aaab2e79dc4aae9f7bce924d77dce5.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/a10eda6a3b4c47d8ae54577ba14db980.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/92a82b5c57f84df2b49c3ff02461f4a2.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/15c6e3d42cac4525a600cfaa0bb56f3c.png)
(Ⅰ)证明:
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/953b687405dd470f8c8e689fb792a85b.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/205e702acfa5443492e490de85abc712.png)
(Ⅱ)若
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/5cea5f5f51ed4f7ab52d20da37c05eb8.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/6450cd136387418c87e9d98aacdd2077.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/ac27ad21c2194557be480869af58a20e.png)
![](https://img.xkw.com/dksih/QBM/2013/4/23/1571194954375168/1571194959855616/STEM/a6ee3d08862f43999129518f0857e1af.png)
您最近一年使用:0次
11-12高三上·甘肃兰州·期末
9 .
已知三棱柱
的侧棱垂直于底面,
,
,
,
,
分别是
,
的中点.
(1)证明:
;
(2)证明:
平面
;
(3)求二面角
的余弦值.
已知三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e98e7edbeab52b0aa5d66396ca46124.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4bf20b186fdaae7736a1d99a7f919.png)
![](https://img.xkw.com/dksih/QBM/2011/2/9/1569977487777792/1569977493086208/STEM/92e17a51-5607-4e57-bb34-aa5b27e4de28.png?resizew=135)
您最近一年使用:0次