1 . 如图,四棱柱
的底面是直角梯形,
,
,
,四边形
和
均为正方形.
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395195597750272/2395577642475520/STEM/d3415e3448824938887b5ba46d998f84.png?resizew=269)
(1)证明:平面
平面
.
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25eb757d05fbff80d50c3bb8dbcb8657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395195597750272/2395577642475520/STEM/d3415e3448824938887b5ba46d998f84.png?resizew=269)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc8946b35564cd277227b80ef05c7f5.png)
您最近一年使用:0次
2020-02-09更新
|
442次组卷
|
3卷引用:云南省楚雄彝族自治州2019-2020学年高三上学期期中数学文科试题
2 . 已知三棱锥
的展开图如图二,其中四边形
为边长等于
的正方形,
和
均为正三角形,在三棱锥
中:
![](https://img.xkw.com/dksih/QBM/2019/9/19/2294011245813760/2294065283833856/STEM/bf6b5548-2c93-491f-b3fc-8fbbd133022d.png)
(1)证明:平面
平面
;
(2)若
是
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/2019/9/19/2294011245813760/2294065283833856/STEM/bf6b5548-2c93-491f-b3fc-8fbbd133022d.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98553247801c03de24cf7e687016e655.png)
您最近一年使用:0次
2019-09-19更新
|
3488次组卷
|
10卷引用:2020届云南省玉溪第一中学高三上学期期中数学(理)试题
2020届云南省玉溪第一中学高三上学期期中数学(理)试题广东省广雅中学、执信、六中、深外四校2020届高三8月开学联考数学理试题广西玉林、柳州市2019-2020学年高三上学期第二次模拟数学(理)试题广东省佛山市荣山中学2019-2020学年高二上学期期中数学试题2020届湖南省株洲市第二中学高三上学期第三次月考数学(理)试题广西柳州市2020届高三第二次模拟考试理科数学试题江西省新余市第四中学2021届高三上学期第一次段考数学(理)试题河北省冀州中学2021届高三上学期第三次月考数学试题江苏省无锡市锡山高级中学2020-2021学年高二下学期期末数学试题(已下线)专题33 空间中线线角、线面角,二面角的求法-学会解题之高三数学万能解题模板【2022版】
名校
3 . 如图,在正方体
中,点
,
分别在棱
,
上,且满足
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/0fa3319b-d01d-4cd7-abcb-78ccd815b406.png?resizew=158)
(1)证明:平面
平面
;
(2)若
,求平面
截正方体
所得截面的面积.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ce78060fece67bbb0a387d06757f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f31a3724c639f88486f8356ca65397.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/0fa3319b-d01d-4cd7-abcb-78ccd815b406.png?resizew=158)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882bc11eba4f28780fc0d928ead2dbbc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee076fe7dbca5616c4e8a6869a355f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
2019-12-12更新
|
320次组卷
|
3卷引用:云南省昆明市2019-2020学年高二下学期期中考试数学(文)试题
名校
4 . 如图,在四棱锥
中,底面
为菱形,平面
底面
,且
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/91db466c-7055-4c3f-bfb8-119a6269a473.png?resizew=203)
(1)证明:
.
(2)求三棱锥
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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98239be016121504e11c8cae78c87e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bae5203f4b4acf23779114b3466e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4dbea6a5faecdd8f6c06cf9fd43a90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/91db466c-7055-4c3f-bfb8-119a6269a473.png?resizew=203)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0180a58a753fced571fc00f0bee8ff0d.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ed9b5930aff911cbecc862a72d7173.png)
您最近一年使用:0次
2019-06-17更新
|
544次组卷
|
3卷引用:【市级联考】云南省楚雄州2018-2019学年高一下学期期中统测数学试题
名校
解题方法
5 . 在三棱柱
中,侧棱
底面
,
分别是
、
、
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/c199368d-abb2-4303-a5df-3b4e141caba5.png?resizew=190)
(Ⅰ)证明:
;
(Ⅱ)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57b7e63faf8ca707fa15413a32abce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7077d7e5ceacb3cd5d7338a8da069c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c709e9fee8d477bddfe595cc760f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/c199368d-abb2-4303-a5df-3b4e141caba5.png?resizew=190)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
(Ⅱ)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2019-07-25更新
|
627次组卷
|
3卷引用:云南省曲靖市罗平县第二中学2019-2020学年高二下学期期中考试数学(理)试题
6 . 如图,在底面为平行四边形的四棱锥
中,过点
的三条棱PA、AB、AD两两垂直且相等,E,F分别是AC,PB的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅱ)求EF与平面PAC所成角的大小.
您最近一年使用:0次
2019-07-04更新
|
3122次组卷
|
9卷引用:云南省曲靖市会泽县第一中学2019-2020学年高二上学期开学考试数学理科试题
云南省曲靖市会泽县第一中学2019-2020学年高二上学期开学考试数学理科试题云南省楚雄师范学院附属中学2020-2021学年高二上学期期中考试数学试题湖北省天门市、仙桃市、潜江市2018-2019学年高一下学期期末考试数学试题(已下线)【新东方】杭州高二数学试卷252河南省实验中学2019-2020学年高一上学期第二次月考数学试题江苏省盐城市东台创新高级中学2019-2020学年高一下学期5月检测数学试题吉林省吉化第一高级中学校2020-2021学年高二11月月考数学(理)试题江苏省常州市武进区礼嘉中学2020-2021学年高二下学期第二次阶段质量调研数学试题(已下线)8.6.2 直线与平面垂直【第二课】“上好三节课,做好三套题“高中数学素养晋级之路
11-12高二·湖南湘西·阶段练习
名校
解题方法
7 . 如图,四凌锥
中,
底面
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/552fd4d0-924d-4bbb-bc73-1e51fa6ddf31.png?resizew=208)
(1)求证:
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ff6d7dd48b57f03d82d2c522ee9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555e29e445c95ddb514840f63fbb1d12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/552fd4d0-924d-4bbb-bc73-1e51fa6ddf31.png?resizew=208)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544381069cb72bed5598ca5adc45ae26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78307cd417504554a4e2276fe24d1162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
您最近一年使用:0次
2019-05-21更新
|
838次组卷
|
3卷引用:【全国百强校】云南省昆明第一中学2018-2019学年高一下学期期中考试数学试题
【全国百强校】云南省昆明第一中学2018-2019学年高一下学期期中考试数学试题(已下线)2011-2012学年湖南省凤凰县华鑫中学高二2月月考文科数学宁夏吴忠市吴忠中学2022-2023学年高二下学期期末考试数学(文)试题
8 . 如图①,在等腰梯形
中,
分别为
的中点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b7ab2a3b321d96a5cf5262894cae81.png)
为
中点,现将四边形
沿
折起,使平面
平面
,得到如图②所示的多面体,在图②中.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/a140e648-85e1-43c6-b28a-b03c9ea32876.png?resizew=315)
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091fee21bbbad43c582d59f959411fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b7ab2a3b321d96a5cf5262894cae81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ca47585273d02911e4eb87f01c8354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c16d99496d31ce4d87301a4793393.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/a140e648-85e1-43c6-b28a-b03c9ea32876.png?resizew=315)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f94b1d943eca1adebf1145b871ef74.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041434f0c90fb3cdd685b8eb1c2b4b26.png)
您最近一年使用:0次
2019-04-14更新
|
2059次组卷
|
8卷引用:云南省昆明市官渡区第一中学2019-2020学年高二下学期期中考试数学(文)试题
云南省昆明市官渡区第一中学2019-2020学年高二下学期期中考试数学(文)试题【市级联考】四川省成都市2019届高三毕业班第二次诊断性检测数学(文)试题【全国百强校】宁夏石嘴山市第三中学2019届高三下学期三模考试数学(文)试题四川省雅安市2021届高三三模数学(文)试题(已下线)2021年全国新高考Ⅰ卷数学试题变式题18-22题四川省绵阳东辰国际学校2020-2021学年高三下学期三诊数学(文)试题(已下线)二轮拔高卷05-【赢在高考·黄金20卷】备战2022年高考数学(文)模拟卷(全国卷专用)四川省泸州市叙永第一中学校2024届高三上学期期末数学(文)试题
12-13高三·安徽黄山·阶段练习
9 . 如图,四边形
为矩形,
平面
,
为
上的点,且
平面
.
![](https://img.xkw.com/dksih/QBM/2013/3/21/1571156547633152/1571156553367552/STEM/58c442c97b744763887b5b47cd92e95a.png?resizew=136)
(1)求证:
;
(2)求三棱锥
的体积;
(3)设
在线段
上,且满足
,试在线段
上确定一点
,使得
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a16404f790cfc370dd89171e2cb8f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://img.xkw.com/dksih/QBM/2013/3/21/1571156547633152/1571156553367552/STEM/58c442c97b744763887b5b47cd92e95a.png?resizew=136)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91cb9a5a14169845d700fbd95890ac.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa711919d767a88b15c3f6dd7fd809a5.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff84ae2da2c81b5c7ccb7e52b40eff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f332555e65843f32f4c623098c6adc72.png)
您最近一年使用:0次
10 . 如图,在直三棱柱
(侧棱垂直于底面)中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/306c52e3-ec60-4d93-b6e6-0dd94f8348df.png?resizew=171)
(1)证明:
平面
;
(2)若
是
的中点,在线段
上是否存在一点
使
平面
?若存在,请确定点
的位置;若不存在,也请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/306c52e3-ec60-4d93-b6e6-0dd94f8348df.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7caa95b00cb6c2d12b1b9eb666cc848d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2019-06-19更新
|
2472次组卷
|
3卷引用:【全国百强校】云南省曲靖市会泽县茚旺高级中学2018-2019学年高一下学期期中考试数学试题
【全国百强校】云南省曲靖市会泽县茚旺高级中学2018-2019学年高一下学期期中考试数学试题(已下线)【新东方】杭州新东方高中数学试卷322四川省遂宁市射洪中学校2022-2023学年高二上学期第一次学月考试数学(理科)试题