名校
解题方法
1 . 如图,三棱柱
的底面
是正三角形,侧面
是菱形,平面
平面
,
,
,
分别是棱
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/1d282724-083f-4bcc-b174-152b3acdcf9b.png?resizew=197)
(1)证明:
平面
;
(2)若
,
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/1d282724-083f-4bcc-b174-152b3acdcf9b.png?resizew=197)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93375ca41cdaac319b79f05108f7fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
您最近一年使用:0次
2022-12-21更新
|
350次组卷
|
4卷引用:广西玉林市部分校2023届高三上学期12月月考数学(文)试题
解题方法
2 . 如图,四棱锥
中,底面
是梯形,
,
,
为等腰直角三角形,
,
为
的中点.
平面
;
(2)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/584a51a3ba7afb65b7648a96c7e8605d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e087b1c89bbbd1af9a17e8b41218accc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c5ace226a547e68702df548b08cb5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
您最近一年使用:0次
3 . 如图所示的多面体,其正视图为直角三角形,侧视图为等边三角形,俯视图为正方形(尺寸如图所示),E为PA的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/9a3621b5-7c5d-4944-a868-b8d6147d7e18.png?resizew=274)
(1)求证:
平面EBD;
(2)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/9a3621b5-7c5d-4944-a868-b8d6147d7e18.png?resizew=274)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02535e1a690ca111ca7a395a1bf48080.png)
您最近一年使用:0次
2022-11-21更新
|
121次组卷
|
2卷引用:广西平果市铝城中学2023-2024学年高二上学期期末模拟数学试题(二)
名校
4 . 某校积极开展社团活动,在一次社团活动过程中,一个数学兴趣小组发现《九章算术》中提到了“刍薨”这个五面体,于是他们仿照该模型设计了一道数学探究题,如图1,E、F、G分别是边长为4的正方形的三边
的中点,先沿着虚线段
将等腰直角三角形
裁掉,再将剩下的五边形
沿着线段EF折起,连接
就得到了一个“刍甍” (如图2)。
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/febe77c0-b267-4764-b29b-3367991132cd.png?resizew=448)
(1)若O是四边形
对角线的交点,求证:
平面
;
(2)若二面角
的大小为
求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe723f84ba0818b496df2a414cc959a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f70627e259fa4e67edff13bb3b4d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4c6641b74b01218e302370ebf71131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654830d1b3b2dc3c6ffcf3654e1d8ac0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/febe77c0-b267-4764-b29b-3367991132cd.png?resizew=448)
(1)若O是四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e826b8202fa0e17245dcc68426c923a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2f83ac39a73f4f01fb8068a0556fa8.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/220de35ee2e51389db38942d3e76584c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2022-11-15更新
|
1642次组卷
|
11卷引用:广西柳州市2023届高三第二次模拟数学(理)试题
广西柳州市2023届高三第二次模拟数学(理)试题山东省青岛市青岛第二中学2022-2023学年高三上学期期中数学试题广东省2023届高三上学期素质评价一数学试题河北省唐山市第一中学2022-2023学年高三上学期12月月考数学试题(已下线)大题强化训练(4)四川省遂宁市射洪中学校2023届高三下学期开学考试理科数学试题广东省揭阳市惠来县第一中学2023届高三最后一模(临门一脚)数学试题广东省佛山市三水区三水中学2022-2023学年高二上学期第二次统考(11月)数学试题辽宁省沈阳市浑南区东北育才学校2023-2024学年高二上学期10月月考数学试题河南省商丘市名校2023-2024学年高二上学期11月期中考试数学试题(已下线)湖南省浏阳市2024届高三上学期12月联考数学试题
名校
5 . 已知四棱锥
的底面
是正方形,侧棱
平面
,点M在棱DP上,且
,点N是在棱PC上的动点(不为端点).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/2268418c-1c33-4464-af53-2fdf136ddefa.png?resizew=231)
(1)若N是棱PC中点,求证:
平面AMN;
(2)若
,当点N在何处时,直线PA与平面AMN所成角的正弦值取得最大值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85ce5e111acf7162b8e1b5a3f6b220.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/2268418c-1c33-4464-af53-2fdf136ddefa.png?resizew=231)
(1)若N是棱PC中点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2304c541406034dd83040e9a7887ed7.png)
您最近一年使用:0次
2022-11-13更新
|
397次组卷
|
3卷引用:广西南宁市第三中学2023届高三模拟(三)数学(理)试题
名校
6 . 如图,在四棱柱
中,
平面
,底面
满足
,
且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/3bcd78c0-a26c-4a5c-aa7e-f34a7e45006e.png?resizew=180)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991451c5002137302527700e195220e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/3bcd78c0-a26c-4a5c-aa7e-f34a7e45006e.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
您最近一年使用:0次
7 . 如图,P为圆锥的顶点,O为圆锥底面的圆心,圆锥的底面直径
,母线
,M是PB的中点,D为OH的中点,四边形OBCH为正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/bba5c179-282d-46df-8e89-27c79597efba.png?resizew=206)
(1)设平面
平面
,证明:
;
(2)设N是线段CD上的一个动点,试确定点N的位置,使得MN与平面PAB所成角的正弦值为
,并求
的比值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91758aec8a689f6a857ea3c289378680.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/bba5c179-282d-46df-8e89-27c79597efba.png?resizew=206)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec0b3e4c789528fe60ac9b8ce990bc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e61111c1e9b98b79615f75540175c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ee6c7e0dfe134561f818cb51eebe09.png)
(2)设N是线段CD上的一个动点,试确定点N的位置,使得MN与平面PAB所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a261474cc7607d31a6324cb4df9c8896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fead487945b39fd9e454a972373a39.png)
您最近一年使用:0次
2022-10-14更新
|
383次组卷
|
2卷引用:广西钦州市第四中学2022-2023学年高二上学期9月月考数学试题
名校
8 . 四棱锥
底面为平行四边形,且
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/47ea1ba2-dc87-4d5a-928e-1e5ba34932aa.png?resizew=232)
(1)点
在棱
上,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
平面
;
(2)若异面直线
与
所成角的余弦值为
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.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/8b99a0a946fda95212b6f5b8970810c2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/47ea1ba2-dc87-4d5a-928e-1e5ba34932aa.png?resizew=232)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ec34fb844a3a9989e1cbf930f138ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2022-10-13更新
|
503次组卷
|
4卷引用:广西壮族自治区百色市平果市铝城中学2023-2024学年高二下学期开学考试数学预测试题
名校
9 . 在如图所示的五面体ABCDFE中,面ABCD是边长为2的正方形,
平面ABCD,
,且
, N为BE的中点,M为CD中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/5ab03a71-30dd-405c-977e-28b7e2ef0f42.jpg?resizew=264)
(1)求证:
平面ABCD;
(2)求二面角
的余弦值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba49c4f6fd70a72785074a7e2d974c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a37e22010bb6d7014272c0d6d355c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/5ab03a71-30dd-405c-977e-28b7e2ef0f42.jpg?resizew=264)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82d5d2beb3dd78baa40ae99a0d7c53.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f7b16888f5e5e3b9745e7725081191.png)
您最近一年使用:0次
2022-10-12更新
|
436次组卷
|
4卷引用:广西壮族自治区梧州市苍梧中学2022-2023学年高二上学期11月期中考试数学试题
名校
10 . 如图,在四棱锥
中,底面
为菱形,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/2d947422-947c-4f38-94f2-225d23d91840.png?resizew=171)
(1)证明:
平面
;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39df09be2183c9b5c2f066bb3f5f938.png)
,
,且
,求平面
与平面
夹角的余弦值.
![](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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ccd2c4b9ef8b0b42ab92635adf7e4a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/2d947422-947c-4f38-94f2-225d23d91840.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39df09be2183c9b5c2f066bb3f5f938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae139b51956b9281d73d9ba82b875e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1365206d14224e0b2d40a7bd8b7965ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-09-28更新
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483次组卷
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4卷引用:广西南宁市邕宁高级中学2023-2024学年高二上学期9月月考数学试题