1 . 如图,在正方体
中,
是
的中点,
是
的中点.
(1)证明:
平面
.
(2)求平面
和平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/26/9c43b6fe-a167-45a1-b3ab-54125e83afc8.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc3f049152c43dd29b12d0a60aa79f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c607775591ff90104cc9c6ce07f919.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2e84d6e368f8368f8301c4cd66d6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
22-23高二·全国·期中
名校
2 . 吴老师发现《九章算术》有“刍甍”这个五面体,于是她仿照该模型设计了一个学探究题,如图:E,F,G分别是正方形的三边AB、CD、AD的中点,先沿着虚线段FG将等腰直角三角形FDG裁掉,再将剩下的五边形ABCFG沿着线段EF折起,连接AB、CG就得到一个“刍甍”.
![](https://img.xkw.com/dksih/QBM/2023/5/31/3249717498044416/3260057908609024/STEM/d2a10473913a41e49daf83711dbcdcef.png?resizew=419)
(1)若
是四边形
对角线的交点,求证:
∥平面
;
(2)若二面角
的大小为
,求直线
与平面
所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2023/5/31/3249717498044416/3260057908609024/STEM/d2a10473913a41e49daf83711dbcdcef.png?resizew=419)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e826b8202fa0e17245dcc68426c923a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7090ad13cf3664c89cdb2288779a9669.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770d42343599d3f26f0e0de8d5849f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732250efe9c8c0cbca127fb2ed2a4bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7090ad13cf3664c89cdb2288779a9669.png)
您最近一年使用:0次
2023-06-15更新
|
306次组卷
|
4卷引用:新疆维吾尔自治区乌鲁木齐市第101中学2022-2023学年高二上学期期末数学试题
新疆维吾尔自治区乌鲁木齐市第101中学2022-2023学年高二上学期期末数学试题(已下线)综合检测(能力篇)-2022-2023学年高二数学同步知识梳理+考点精讲精练(人教B版2019选择性必修第一册)重庆市第十一中学校2022-2023学年高二下学期期中数学试题(已下线)第11讲 第一章 空间向量与立体几何 章末题型大总结(1)
3 . 如图,四棱锥
的底面
是梯形,
,
,E为AD延长线上一点,
平面
,
,
,F是PB中点.
(1)证明:
;
(2)若
,三棱锥
的体积为
,求锐二面角
的余弦值.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.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/885020440f20b5fc2f91ac373ffa004e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60023f7a8c7310dfad0b55a5266977c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/fbc31e23-168a-4b75-a21d-e0759a348e12.png?resizew=144)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2484662ae40c406b054d14a7f9e118.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ea9d92e5c258a50af1e461c7388894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4188199c6db7e447f1b642e4997044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bfc65bfbc357d43069e9aad18f8625.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在四棱锥
中,
底面
是直角梯形,
,点
是
的中点.
(1)证明:平面
平面
;
(2)若直线
与平面
所成角的正弦值为
,求平面
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/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654c6391665a5aee872901309abd4b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ae63398c7f9e426864e1bf5bb74942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/23/92d3de6a-c309-4128-9dfa-e27791a66b4f.png?resizew=179)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
2023-10-07更新
|
2393次组卷
|
18卷引用:新疆生产建设兵团第六师五家渠高级中学2022-2023学年高二上学期期末数学试题
新疆生产建设兵团第六师五家渠高级中学2022-2023学年高二上学期期末数学试题重庆市铜梁一中等三校2022-2023学年高二上学期期末数学试题山西省阳泉市2022-2023学年高二上学期期末数学试题宁夏银川市贺兰县第二高级中学2022-2023学年高一下学期期末数学试题黑龙江省佳木斯市第一中学2021-2022学年高一下学期期末考试数学试题四川省成都市棠湖外国语学校2023-2024学年高二上学期期末模拟质量检测数学试题四川省宜宾市叙州区第一中学校2023-2024学年高二上学期期末数学试题湖南省常德市桃源县第一中学2022-2023学年高三上学期8月月考数学试题山西省运城市景胜中学2022-2023学年高二上学期11月月考数学(A)试题福建省南平市四校2023届高三下学期3月联考数学试题湖南省长沙市雅礼中学2023届高三下学期月考(八)数学试题山东省日照实验高级中学2023届高三模数学试题山东省济宁市实验中学2022-2023学年高一下学期6月月考数学试题福建省福清第一中学2024届高三上学期10月月考数学试题云南省曲靖市第一中学2024届高三上学期阶段性检测(四)数学试题重庆市第七中学校2023-2024学年高二上学期期中考试数学试题河南省驻马店市驻马店高级中学2023-2024学年高二上学期期中数学试题四川省绵阳南山中学实验学校2023-2024学年高二上学期12月月考数学试题
5 . 如图,在四棱锥
中,
平面
,
,点
是线段
中点.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
平面
;
(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/f95475bfc06e884754eb4a455c3f434e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0136856c425c53510fdd52c86bca8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8277767aa2d4369a8c2deb6d16f08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/2/8734b203-6427-4a7c-9b72-8f8477148c63.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f4096ff62b4f29932cd8c6eef661a3.png)
您最近一年使用:0次
2023-08-02更新
|
714次组卷
|
2卷引用:新疆乌鲁木齐市米泉中学(原米泉市一中分校)2022-2023学年高二上学期期末数学试题
名校
6 . 如图,在正方体
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/12/27/3139931745837056/3141205454979072/STEM/c953ef931ac645599dcfa7249186614f.png?resizew=195)
(1)求证:
平面
;
(2)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2022/12/27/3139931745837056/3141205454979072/STEM/c953ef931ac645599dcfa7249186614f.png?resizew=195)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231673dd67ab79d3c5da73904ceade1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b3b4c5ce7aca81becc07ed4903736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
您最近一年使用:0次
2022-12-29更新
|
230次组卷
|
3卷引用:新疆喀什地区巴楚县第五中学等3校2022-2023学年高二上学期1月期末考试数学试题
11-12高二上·广东·期末
名校
解题方法
7 . 如图,四棱锥
的底面
是矩形,
⊥平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/2921a67f-aa9c-4c68-988e-ff0c43e53be0.png?resizew=153)
(1)求证:
⊥平面
;
(2)求二面角
余弦值的大小;
(3)求点
到平面
的距离.
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46571701ccaa18d3c844ab99ee6c30e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/2921a67f-aa9c-4c68-988e-ff0c43e53be0.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d9f756419912dd298a0d6857130c80.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2023-04-18更新
|
1330次组卷
|
27卷引用:新疆伊西哈拉镇中学2018-2019学年高二上学期期末数学试卷
新疆伊西哈拉镇中学2018-2019学年高二上学期期末数学试卷(已下线)2010-2011学年广东北江中学第一学期期末考试高二理科数学河北省邢台市巨鹿县二中2017-2018学年高二下学期期末考试数学(理)试题福建省福州福清市2017-2018学年学年高二上学期期末考试数学(理)试题北京市对外经济贸易大学附属中学(北京市第九十四中学)2023届高三上学期数学期末复习试题陕西省榆林市府谷中学2022-2023学年高二上学期期末线上考试理科数学试题北京市育英学校2021-2022学年高二普通班上学期期末练习数学试题天津市河东区2024届高三上学期期末质量调查数学试题(已下线)2012-2013学年福建省三明一中高二上学期期中考试理科数学试卷(已下线)2012—2013学年甘肃省甘谷一中高二上学期期中考试理科数学试卷(已下线)2012-2013学年湖南邵阳石齐学校高二第三次月考理科数学试卷湖南省长沙市第一中学2015-2016学年高一12月月考数学试题【校级联考】江西省南昌市八一中学、洪都中学、麻丘高中等七校2018-2019学年高二下学期期中考试数学(文)试题四川省棠湖中学2019-2020学年高二上学期开学考试数学(理)试题天津市第二十五中学2020-2021学年高二上学期期中数学试题海南省东方市东方中学2021-2022学年高二上学期第二次月考数学试题江苏省南京市第一中学实验学校2022-2023学年高二下学期期中数学试题第三章空间向量与立体几何 单元练习-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册福建省泉州市晋江二中、鹏峰中学、广海中学、泉港区第五中学2022-2023学年高二上学期期中联考数学试题北京市育英学校2022-2023学年高二下学期期中练习数学试题北京市昌平区首都师范大学附属回龙观育新学校2022-2023学年高二上学期10月月考数学试题北京市育英学校2024届高三上学期统一练习(一) 数学试题陕西省西安南开高级中学2023-2024学年高二上学期9月第一次质量检测数学试题北京市怀柔区青苗学校2023-2024学年高二上学期期中考试数学试题湖北省部分高中联考协作体2023-2024学年高二上学期期中联考数学试题(已下线)高三数学开学摸底考(天津专用)(已下线)黄金卷07
名校
解题方法
8 . 如图,在棱长为2的正方体
中,点M为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/c4111e02-113d-4ae8-bd74-89c43e25fef0.png?resizew=148)
(1)求证:
;
(2)求平面
与平面
夹角的余弦值;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/c4111e02-113d-4ae8-bd74-89c43e25fef0.png?resizew=148)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e862713d078c4f06ec1f15ccd6f5a1f7.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1774d0570a0ecfcdeb274828d7f4a769.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1774d0570a0ecfcdeb274828d7f4a769.png)
您最近一年使用:0次
2022-11-10更新
|
368次组卷
|
4卷引用:新疆泽普县第二中学2022-2023学年高二上学期期末考试数学试题
名校
9 . 如图,在三棱柱
中,侧面
为矩形,平面
平面
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/f950cd55-f20a-4155-ad11-690d248969e2.png?resizew=234)
(1)求证:
平面
;
(2)若侧面
是正方形,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047f00a89d08e79d45adde46af70c9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddef39ef9ed3da136c4ed8b5d28b73e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/f950cd55-f20a-4155-ad11-690d248969e2.png?resizew=234)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2022-12-04更新
|
542次组卷
|
4卷引用:新疆阿克苏市实验中学2022-2023学年高二上学期期末考试数学试题
10 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
平面
,
,正方形
的对角线交于点O.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/4f712b14-1d2e-496f-8663-267016b2f919.png?resizew=134)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
平面PAC;
(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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801cabc43c024b9c5fac34b7db5d69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/4f712b14-1d2e-496f-8663-267016b2f919.png?resizew=134)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
您最近一年使用:0次
2022-11-18更新
|
795次组卷
|
3卷引用:新疆五家渠市兵团二中金科实验中学2022-2023学年高一下学期期末考试数学试题(二)(问卷)
新疆五家渠市兵团二中金科实验中学2022-2023学年高一下学期期末考试数学试题(二)(问卷)青海省玉树州三校(二高、三高、五高)2021-2022学年高二下学期期末联考数学(理科)试题(已下线)2023年北京高考数学真题变式题16-21