1 . 已知平面
两两垂直,直线
满足:
,则直线
可能满足以下关系:①两两相交;②两两垂直;③两两平行;④两两异面.其中所有正确结论的编号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5edf364489a24e6f4e8926291d3060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.①③ | B.②④ |
C.①②④ | D.①②③④ |
您最近一年使用:0次
2 . 如图,已知平面
平面
,直线
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3be7a04b-5c65-4134-9172-4389b0db7d66.png?resizew=156)
(1)求证:
平面
;
(2)若
,
平面
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd654221ab95fe241d9e0202443f2609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55084a713700c8acf54121295ccd269.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3be7a04b-5c65-4134-9172-4389b0db7d66.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70301b6c9afa595b49463a8c151bfe71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d11a5a756d8fdd7b294c4f5fd63467b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1100a56e918f75ed6d955a802050f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b10f890a5f9bc9140286f8326398d16.png)
您最近一年使用:0次
2020-06-12更新
|
663次组卷
|
5卷引用:山东省德州市2020届高三第二次(6月)模拟考试数学试题
山东省德州市2020届高三第二次(6月)模拟考试数学试题(已下线)数学-6月大数据精选模拟卷05(北京卷)(满分冲刺篇)(已下线)专题九 立体几何与空间向量-山东省2020二模汇编(已下线)专题16 立体几何-2020年高考数学母题题源解密(北京专版)山东省高考联盟2020-2021学年高三下学期开学收心考试数学试题
名校
3 . 如图所示,四边形
为菱形,
,二面角
为直二面角,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/3a39b888-d849-4888-b4ae-28da87670b13.png?resizew=233)
(Ⅰ)求证:
;
(Ⅱ)若
,当二面角
的余弦值为
时,求直线
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d399d731913a563e291b817831a0c678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/3a39b888-d849-4888-b4ae-28da87670b13.png?resizew=233)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc56fdf70e65bd88980c64af96b83da.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d141e18938319cc05063d29c111557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2020-06-09更新
|
508次组卷
|
4卷引用:2020年浙江省名校高考预测冲刺卷(三)
名校
解题方法
4 . 在矩形ABCD中,
,
,沿矩形对角线BD将
折起形成四面体ABCD,在这个过程中,现在下面四个结论:①在四面体ABCD中,当
时,
;②四面体ABCD的体积的最大值为
;③在四面体ABCD中,BC与平面ABD所成角可能为
;④四面体ABCD的外接球的体积为定值.其中所有正确结论的编号为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df6d51738ac1bc8b9530ea4a55745c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62d52be7c6e607972b4cf8ccbf58436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a316c27ccf35e5e9b4294364985927dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
A.①④ | B.①② | C.①②④ | D.②③④ |
您最近一年使用:0次
2020-06-08更新
|
1022次组卷
|
6卷引用:辽宁省抚顺市六校(省重点)联合体2020届高三5月联考数学(理科)试题
5 . 如图,在平行四边形ABCD中,沿其对角线BD将
折起至
,使得点
在平面ABCD内的射影恰为点B,点E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/803d83b2-adec-4fa9-9ff6-80b6525ee217.png?resizew=216)
(Ⅰ)求证:
平面BDE;
(Ⅱ)若
,求
与平面BDE所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a9ec45721f7b4d1c99917ac0d970f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46cea1f4861584aba9b0d551961c8fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/803d83b2-adec-4fa9-9ff6-80b6525ee217.png?resizew=216)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0091fa6d70662a7b3edc5e395c2be253.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff29971ccc633d89832ffa9bd54afa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900b844294e8c07ea9a858adb845121c.png)
您最近一年使用:0次
6 . 如图,在四棱锥
中,底面ABCD为矩形,
,
,侧面SAD是以AD为斜边的等腰直角三角形,且平面
平面ABCD,M,N分别为AD,SC的中点.
![](https://img.xkw.com/dksih/QBM/2020/5/27/2471781569937408/2472410243121152/STEM/171d28e4-31db-4544-883d-74db14e9128f.png)
(1)求证:
平面SAB.
(2)求直线BN与平面SAB所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.png)
![](https://img.xkw.com/dksih/QBM/2020/5/27/2471781569937408/2472410243121152/STEM/171d28e4-31db-4544-883d-74db14e9128f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
(2)求直线BN与平面SAB所成角的余弦值.
您最近一年使用:0次
7 . 如图,在四棱锥
中,四边形
是等腰梯形,
,
,
,三角形
是等边三角形,平面
平面
,
、
分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/1c433b7f-2c7d-4d1b-b037-4708e859c6db.png?resizew=195)
(1)求证:平面
平面
;
(2)若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.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/c15416b74b2ecbcfa38cf34a9ffff730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae139b51956b9281d73d9ba82b875e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448cbac9a1ef3de7538a6b30cdc39582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/1c433b7f-2c7d-4d1b-b037-4708e859c6db.png?resizew=195)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b156bc439fbaba3bfc9937beccb9b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ce281401b92d11871867cf5a5fe199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0421a60cf7269fd9869c77c59a84d2a1.png)
您最近一年使用:0次
20-21高二·全国·课后作业
8 . 如图,已知,在
与
的交线上取线段
,且AC,BD分别在平面
和平面
内,它们都垂直于交线AB,并且
,
,求CD的长.
您最近一年使用:0次
2020-01-31更新
|
204次组卷
|
4卷引用:人教B版(2019) 必修第四册 逆袭之路 第十一章 立体几何初步 11.4.2 平面与平面垂直
人教B版(2019) 必修第四册 逆袭之路 第十一章 立体几何初步 11.4.2 平面与平面垂直(已下线)第十一章 立体几何初步 11.4 空间中的垂直关系 11.4.2 平面与平面垂直人教B版(2019)必修第四册课本习题11.4.2 平面与平面垂直(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)
解题方法
9 . 如图,在五面体
中,
平面
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/3aa129ef-2b28-46ff-add4-0a0b8a6bbdd8.png?resizew=166)
(1)求证:
;
(2)若
,且二面角
的大小为60°,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292d0b9ce587bd5df884a988c22ccba2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/3aa129ef-2b28-46ff-add4-0a0b8a6bbdd8.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59bc3943c9bc08400c3751b31c7ce00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed047df6b180b77f6653b277c174a551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
您最近一年使用:0次
2020-05-25更新
|
212次组卷
|
2卷引用:2020届福建省厦门市高三质量检查(5月二模)数学(文)试题
10 . 已知
中,
,
,
.如图,点
为斜边
上一个动点,将
沿
翻折,使得平面
平面
.当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
______ 时,
取到最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86648fdbd414f8d4c090207b8ade74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427b94ae85213281993e0e53ff330744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020ebe1219437129358b986eb9e70bbf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/80a2404a-67b6-40f7-bc75-210fdc6ef897.png?resizew=390)
您最近一年使用:0次