1 . 在如图所示的几何体中,四边形
是等腰梯形,
∥
,
平面
.
(Ⅰ)求证:
平面
;
(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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6fa70b88c1b619f9044e8488e8b1ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb78cfe939324896f01fd245149aa063.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9d40f58f5fd5fb401a529a42b93ff1.png)
![](https://img.xkw.com/dksih/QBM/2012/6/20/1570893451526144/1570893457178624/STEM/1a2f3b6b-3352-4758-a219-14d4a78a5ee3.png)
您最近一年使用:0次
2019-01-30更新
|
4165次组卷
|
17卷引用:广东省广州市华南师范大学附属中学2018届高三综合测试(二) 理科数学试卷
广东省广州市华南师范大学附属中学2018届高三综合测试(二) 理科数学试卷2012年全国普通高等学校招生统一考试理科数学(山东卷)(已下线)2014届湖南省长沙市高考二模文科数学试卷2015-2016学年广东省揭阳市惠来一中等高二上学期期末理科数学试卷2015-2016学年广东省惠来一中、揭东一中高二上期末理科数学试卷广西防城港市2018届高中毕业班1月模拟考试数学(理)试题(已下线)同步君人教A版必修2第二章2.3.4直线与平面垂直的性质高中数学人教版 必修2 第二章 点、直线、平面之间的位置关系 2.3.4平面与平面垂直的性质2018-2019学年高中数学必修2人教版:评估验收卷(二)湖南省醴陵市第一中学2018-2019学年高二上学期期末考试数学(理)试题新疆维吾尔自治区石河子市第二中学2018-2019学年高一上学期期末考试数学试题江苏省连云港市赣榆区智贤中学2019-2020学年高一下学期5月月考数学试题广西壮族自治区田阳高中2019-2020学年高二6月月考数学(理)试题人教B版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 本章复习提升安徽省池州市东至县第三中学2020-2021学年高二上学期期中理科数学试题山西省怀仁市第一中学校云东校区2021-2022学年高一下学期第三次月考数学(理)试题江西省抚州市南城县第二中学2022-2023年高二下学期第一次月考数学试题
2 . 如图,在多面体
中,
平面
,直线
与平面
所成的角为30°,
为
的中点.
(Ⅰ)求证:平面
平面
;
(Ⅱ)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4776a94ae2625c37aabbfd5fb952f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e537ded362ccca2507a574af1f4f8feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0fbe03367e014e2f2af034448f45da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba1f30ef2ee669b79ee29be260876e9.png)
![](https://img.xkw.com/dksih/QBM/2018/4/25/1931786550263808/1936464351272960/STEM/c98fc09b682e4f5e880355af239db6a8.png?resizew=152)
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3 . 如图,四边形
是矩形,沿对角线
将
折起,使得点
在平面
上的射影恰好落在边
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/40949aeb-c046-4eee-b6e4-0443830d7589.png?resizew=353)
(1)求证:平面
平面
;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/40949aeb-c046-4eee-b6e4-0443830d7589.png?resizew=353)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8eb3a83ac62333bf3f8f893e3475126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
您最近一年使用:0次
2018-03-30更新
|
1959次组卷
|
7卷引用:广东省广雅中学2018-2019学年高三上学期期中数学(理)试题
广东省广雅中学2018-2019学年高三上学期期中数学(理)试题安徽省安庆市2018届高三二模考试理科数学试题【全国市级联】河南省洛阳市2018届高三第三次统一考试数学(理)试卷安徽省宿州市砀山县第二中学2019-2020学年高三上学期第四次月考数学(文)试题2(已下线)专题02 各类角的证明与求解(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖贵州省思南中学2019-2020学年高二上学期期末考试数学(理)试题(已下线)选择性必修第一册模块检测卷(能力提升)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第一册)
名校
4 . 三棱锥被平行于底面ABC的平面所截得的几何体如图所示,截面为A1B1C1,∠BAC=90°,A1A⊥平面ABC,A1A=
,AB=
,AC=2,A1C1=1,
.
(1)证明:BC
A1D;
(2)求二面角A-CC1-B的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0870515b612ef842f01f3b5eeca220b5.png)
(1)证明:BC
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(2)求二面角A-CC1-B的余弦值.
![](https://img.xkw.com/dksih/QBM/2018/3/6/1896189515472896/1903293946019840/STEM/d95a5686-1951-4424-b8ac-4229e9b94db3.png)
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2018-03-16更新
|
496次组卷
|
6卷引用:广东省汕头市澄海中学2021届高三上学期第一次段考数学试题
5 . 如图,将一副三角板拼接,使他们有公共边BC,且使这两个三角形所在的平面互相垂直,
,
,
,BC=6.
(1)证明:平面ADC平面ADB;
(2)求二面角A—CD—B平面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8aa3537e68d5de3c136469936c3254b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfac9ab1dc776c9ec076ab2a132fcd2.png)
(1)证明:平面ADC平面ADB;
(2)求二面角A—CD—B平面角的正切值.
![](https://img.xkw.com/dksih/QBM/2018/3/2/1893344296435712/1896159024537600/STEM/9e65728ba1fd448493660ccfad29db93.png?resizew=233)
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2018-03-06更新
|
469次组卷
|
4卷引用:广东省深圳市南山区2018届高三上学期期末教学质量监测数学(理)试题
6 . 已知长方体
中,
为
的中点,如图所示.
![](https://img.xkw.com/dksih/QBM/2018/1/13/1859384442798080/1860410354827264/STEM/489b731f1c7b4081935bbc0a2d348d26.png?resizew=257)
(1) 证明:
平面
;
(2) 求平面
与平面
所成锐二面角的大小的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e1fad76eea484754933db9b3d3f4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35957ef7d9ded9c24f1419ed85332963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39141d487ab0d4021ea5858f4af189f8.png)
![](https://img.xkw.com/dksih/QBM/2018/1/13/1859384442798080/1860410354827264/STEM/489b731f1c7b4081935bbc0a2d348d26.png?resizew=257)
(1) 证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4b62d15ef50c2d9bb8461c7507bd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a52dca906792e862be231225d450b1.png)
(2) 求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c4c4511ff6cec33b6bf5c07b8f4c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a52dca906792e862be231225d450b1.png)
您最近一年使用:0次
7 . 如图,四边形
是矩形,
,
,
,
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6806da8debac8ab466f53bbd4843499f.png)
![](https://img.xkw.com/dksih/QBM/2017/9/22/1779399792500736/1779525896421376/STEM/8fb6f7caefd743d1859a7c64864ec731.png?resizew=218)
(1)求证:
;
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e7b83a2497d1662d1a95ec4cbb7495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6806da8debac8ab466f53bbd4843499f.png)
![](https://img.xkw.com/dksih/QBM/2017/9/22/1779399792500736/1779525896421376/STEM/8fb6f7caefd743d1859a7c64864ec731.png?resizew=218)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
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8 . 如图,正三棱柱
的各条棱长均相等,
为
的中点,
分别是线段
和线段
上的动点(含端点),且满足
.当
运动时,下列结论中不正确的是
![](https://img.xkw.com/dksih/QBM/2017/12/10/1835658736246784/1836258946686976/STEM/f498e583c2c245a4a4baead60339666b.png?resizew=122)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea245109473c8336e716922b3d3bd7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://img.xkw.com/dksih/QBM/2017/12/10/1835658736246784/1836258946686976/STEM/f498e583c2c245a4a4baead60339666b.png?resizew=122)
A.平面![]() ![]() | B.三棱锥![]() |
C.![]() | D.平面![]() ![]() ![]() |
您最近一年使用:0次
2017-12-11更新
|
777次组卷
|
4卷引用:广东省广雅中学2018-2019学年高三上学期期中数学(理)试题
真题
9 . 如图,在底面是直角梯形的四棱锥
中,
面
.
(1)求四棱锥
的体积;
(2)求面
与面
所成的二面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9280677503247b115b2b704e9c871f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba5651b1e7bcf9255004d9845286e19.png)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
(2)求面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2a52f691259e1a747d356f631c3d3c.png)
您最近一年使用:0次
2022-11-09更新
|
585次组卷
|
4卷引用:2001年普通高等学校招生考试数学试题(广东卷)
2001年普通高等学校招生考试数学试题(广东卷)2001年普通高等学校招生考试数学(理)试题(全国卷)2001年普通高等学校招生考试数学(文)试题(全国卷)(已下线)第四章 立体几何解题通法 专题二 体积法 微点1 体积法(一)【基础版】
10 . 如图,四棱锥
中,
平面
,底面
为正方形,且
.
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/f83a04565a8ebaa111894b724b0ba266.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/b63203fb-89ac-4494-9351-711e02a3fce4.png?resizew=217)
您最近一年使用:0次