1 . 一个长方体的平面展开图及该长方体的直观图的示意图如图所示.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
标记在长方体相应的顶点处(不需说明理由);
(2)在长方体中,判断直线
与平面
的位置关系,并证明你的结论;
(3)在长方体中,设
的中点为
,且
,
,求证:
平面
.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
(2)在长方体中,判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55a8898c347a62c7de2bdca3f3c7e33.png)
(3)在长方体中,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338c6c83ab4abc895ac36ab888a55be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53569e6ec795658b4fffcddeebe0f142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
您最近一年使用:0次
2 . 在直三棱柱ABC﹣A1B1C1中,BC=CC1,AB⊥BC.点M,N分别是CC1,B1C的中点,G是棱AB上的动点.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287347712/STEM/af60347b036b43508ebf6a5d8329bcd1.png)
(Ⅰ)求证:B1C⊥平面BNG;
(Ⅱ)若CG∥平面AB1M,试确定G点的位置,并给出证明.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287347712/STEM/af60347b036b43508ebf6a5d8329bcd1.png)
(Ⅰ)求证:B1C⊥平面BNG;
(Ⅱ)若CG∥平面AB1M,试确定G点的位置,并给出证明.
您最近一年使用:0次
3 . 如图,四棱锥
的底面是矩形,
底面
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/20/7c14cea3-fd94-4c66-b3e0-f8b8eef6a7e4.png?resizew=160)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
平面
;
(2)证明:
;
(3)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffddeafce03aae663bc823e2d5127c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/20/7c14cea3-fd94-4c66-b3e0-f8b8eef6a7e4.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6c62979a7aa534a191d8387a741e8.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
您最近一年使用:0次
解题方法
4 . 如图,在所有棱长都等于1的三棱柱ABC-A1B1C1中,∠ABB1=
,∠B1BC=
.
(1)证明:A1C1⊥B1C;
(2)求直线BC与平面ABB1A1所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/25/0facd045-f6aa-4dbe-9097-3f26da4f00ec.png?resizew=167)
(1)证明:A1C1⊥B1C;
(2)求直线BC与平面ABB1A1所成角的大小.
您最近一年使用:0次
2023-11-23更新
|
457次组卷
|
3卷引用:广东省阳江市2023-2024学年高二上学期1月期末测试数学试题
广东省阳江市2023-2024学年高二上学期1月期末测试数学试题江苏省南京市2023-2024学年高二上学期期中调研测试数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点5 直线与平面所成角综合训练【培优版】
5 . 如图1,在直角三角形
中,
为直角,
在
上,且
,作
于
,将
沿直线
折起到
所处的位置,连接
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/a490ef69-6007-4cfd-b1c3-777a8de61b1a.png?resizew=454)
(1)若平面
平面
,求证:
;
(2)若二面角
为锐角,且二面角
的正切值为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f859d73bc9ef3159cca595c73a524cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673a2a8c516b154fb34109f7a17555dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5cf9e5f493f8cc9bd441d928b2d25e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c3cc1f331dbb2248b0829039df7f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/a490ef69-6007-4cfd-b1c3-777a8de61b1a.png?resizew=454)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac48b9ac8efbf41d6ab5242d247bd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03d3b1a7b201f380f960db4b6ff2943.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966903d099ea0534ab7019d9346f89c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1f04ff8d19d4a3e0ffe4504b961b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c76e558109d9b8dd700c1a7f9cc73ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
您最近一年使用:0次
2022-12-16更新
|
1855次组卷
|
7卷引用:广东省深圳市高级中学2022-2023学年高二下学期开学考试数学试题
广东省深圳市高级中学2022-2023学年高二下学期开学考试数学试题浙江省丽水市青田县船寮高级中学2021-2022学年高一下学期第二次月考数学试题浙江金华第一中学2022-2023学年高三下学期3月月考数学试题(已下线)专题10 空间角、距离的计算-期中期末考点大串讲(苏教版2019必修第二册)安徽省马鞍山市红星中学2022-2023学年高一下学期5月月考数学试卷湖北省武汉市第十一中学2022-2023学年高一下学期6月月考数学试题(已下线)专题3 由二面角求线段长问题(解答题一题多解)
名校
解题方法
6 . 如图,在三棱柱
中,
平面
,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/c79735a0-9659-4d9d-9ea7-c15604eec8b9.png?resizew=144)
(1)求证:
;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe312c442d13f937a286c0ed069d6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61ef77be3243e46e5591c4bc4c99942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/6655cc150ddc9deba2254780984d0024.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/c79735a0-9659-4d9d-9ea7-c15604eec8b9.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b500528c1f0ed3a48e63a44788b9956.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
您最近一年使用:0次
2022-10-29更新
|
404次组卷
|
4卷引用:广东省开平市第一中学2022-2023学年高二上学期10月月考数学试题
解题方法
7 . 如图,在正四棱柱
中,底面边长为2,高为4.
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076206146207744/3081326282309632/STEM/f2806797176c486bb76057e7768dd70d.png?resizew=233)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a0e00113872f921116b6c0c3177d0f.png)
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076206146207744/3081326282309632/STEM/f2806797176c486bb76057e7768dd70d.png?resizew=233)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a0e00113872f921116b6c0c3177d0f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
2022-10-05更新
|
946次组卷
|
5卷引用:广东省湛江市雷州市白沙中学2022-2023学年高二上学期第一次月考数学试题
名校
8 . 如图,在四棱锥
中,平面
平面
,四边形
是边长为2的菱形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/7a27efab-0905-47af-8083-aef2eba0e679.png?resizew=163)
(1)求证:
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/7a27efab-0905-47af-8083-aef2eba0e679.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd5c41c921836b50f8e18abfdc5df3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2022-07-12更新
|
1235次组卷
|
2卷引用:广东省广州市七区2021-2022学年高二下学期期末数学试题
名校
解题方法
9 . 如图,四棱锥
的底面是边长为a正方形,每条侧棱长都是底面边长的
倍,P为侧棱SD上的点.
![](https://img.xkw.com/dksih/QBM/2022/5/15/2979504463380480/2981509862113280/STEM/ae5fee007ccb4d81881e29449c9bae47.png?resizew=191)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c177e06cc3f703e8ca7be7c491fa2942.png)
(2)若
,侧棱SC上是否存在一点E,使得
,若存在,求
的值,若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2022/5/15/2979504463380480/2981509862113280/STEM/ae5fee007ccb4d81881e29449c9bae47.png?resizew=191)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c177e06cc3f703e8ca7be7c491fa2942.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb446da7614cc62fd0f5c041ae403807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e58abb2fa685b7dfe6ca8fbb3543ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9013fec36586592a57b9abfb6ce4ffa.png)
您最近一年使用:0次
2022-05-17更新
|
620次组卷
|
6卷引用:广东省佛山市顺德区华侨中学2021-2022学年高二上学期期中数学试题
解题方法
10 . 如图所示,在矩形
中,
,
,
为
的中点,沿
将△
翻折,使二面角
为直二面角.
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879458204426240/2880095439290368/STEM/7748ca21-eb0b-481c-a3cb-d5f4de119ac5.png?resizew=431)
(1)求证:
;
(2)求
与平面
所成角的大小;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdd9f345915ae742ed3dcd3f9678264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18a490a22cac27417ddc794f00a1941.png)
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879458204426240/2880095439290368/STEM/7748ca21-eb0b-481c-a3cb-d5f4de119ac5.png?resizew=431)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151e948feebdf7b91fbe739feafa9bc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164e1cc74e41a2a55d3767c006392bfd.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db1d8f228c87b65a3609f825fc441d5.png)
您最近一年使用:0次
2021-12-25更新
|
700次组卷
|
2卷引用:广东省广州思源学校2022-2023学年高二上学期10月月考数学试题