1 . 在如图所示的多面体中,四边形
和
都为矩形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/08e60bae-4c50-46a1-80e2-691ec35ce1ed.png?resizew=169)
(Ⅰ)若
,证明:直线
平面
;
(Ⅱ)设
,
分别是线段
,
的中点,在线段
上是否存在一点
,使直线
平面
?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/08e60bae-4c50-46a1-80e2-691ec35ce1ed.png?resizew=169)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(Ⅱ)设
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a7494edc88340385272679347b6af2.png)
您最近一年使用:0次
2016-12-03更新
|
6839次组卷
|
14卷引用:重庆市铜梁县第一中学2017-2018学年高二10月月考数学(理)试题
重庆市铜梁县第一中学2017-2018学年高二10月月考数学(理)试题2014年全国普通高等学校招生统一考试文科数学(四川卷)四川省乐山市十校2019-2020学年高二上学期期中数学(文)试题江西省山江湖协作体2019-2020学年高二上学期第三次月考(自招班)数学试题湖南省常德市石门县第二中学2018-2019学年高一下学期第一次月考数学试题山东省菏泽市2019-2020学年高一下学期期中考试数学试题A四川省阆中中学2020届高三全景模拟(最后一考)数学(文)试题江西省宜春市上高县第二中学2019-2020学年高二下学期期末考试数学(文科)试题(已下线)专题19 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅰ专版)云南省曲靖市第二中学2021届高三二模数学(文)试题河南省郑州市新密市第一高级中学2020-2021学年高二下学期期末数学文科试题(已下线)第五章 破解立体几何开放探究问题 专题一 立体几何存在性问题 微点1 立体几何存在性问题的解法(一)【基础版】(已下线)专题23 立体几何解答题(文科)-3(已下线)【一题多解】存在与否 向量探索
真题
2 . 四棱锥S—ABCD中,底面ABCD为平行四边形,侧面SBC⊥底面ABCD,已知
∠ABC = 45°,AB=2,BC=
,SA=SB =![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)证明SA⊥BC;
(2)求直线SD与平面SAB所成角的大小.
∠ABC = 45°,AB=2,BC=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)证明SA⊥BC;
(2)求直线SD与平面SAB所成角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/30/7a2a847a-2350-4732-a70c-b146a0a8a808.png?resizew=167)
您最近一年使用:0次
2016-11-30更新
|
1863次组卷
|
5卷引用:重庆市缙云教育联盟2022-2023学年高二下学期期末数学试题
真题
3 . 如图,四棱锥
中,底面
为矩形,
底面
,
,点
是
的中点.
(1)证明:
平面
;
(2)若
,求二面角
的平面角的余弦值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f235e99b0b55ac252c4b18cc315dc114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f06184f021ac21d72de1c7f55b0778.png)
![](https://img.xkw.com/dksih/QBM/2010/6/17/1569762502721536/1569762507636736/STEM/b712794a-6a41-4b0d-807a-6276157b5e22.png?resizew=143)
您最近一年使用:0次
2016-11-30更新
|
1685次组卷
|
4卷引用:2010年普通高等学校招生全国统一考试(重庆卷)数学(文科)
2010年普通高等学校招生全国统一考试(重庆卷)数学(文科)(已下线)2012届甘肃省西北师大附中高三第一次诊断文科数学试卷2016届山东省实验中学高三第一次模拟理科数学试卷2015-2016学年湖北沙市中学高二下第六次半月考理数学卷
10-11高二下·重庆·阶段练习
4 . 如图,在斜边为AB的Rt△ABC,过A作PA⊥平面ABC,AE⊥PB于E,AF⊥PC于F.
![](https://img.xkw.com/dksih/QBM/2011/4/13/1570117697257472/1570117702590464/STEM/7f17ff3f67db4eba802e4150f08f625a.png?resizew=165)
(1)求证:BC⊥平面PAC.
(2)求证:PB⊥平面AEF.
(3)若AP=AB=2,试用tanθ(∠BPC=θ)表示△AEF的面积,当tanθ取何值时,△AEF的面积最大?最大面积是多少?
![](https://img.xkw.com/dksih/QBM/2011/4/13/1570117697257472/1570117702590464/STEM/7f17ff3f67db4eba802e4150f08f625a.png?resizew=165)
(1)求证:BC⊥平面PAC.
(2)求证:PB⊥平面AEF.
(3)若AP=AB=2,试用tanθ(∠BPC=θ)表示△AEF的面积,当tanθ取何值时,△AEF的面积最大?最大面积是多少?
您最近一年使用:0次
12-13高三·湖北·阶段练习
名校
5 . 如图1四边形
中,
是
的中点,
将图1沿直线
折起,使得二面角
为60°.如图2.
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959373361152/1572959379636224/STEM/9d6ae5f5c93441ac939c06f0af5049e5.png)
(1)求证:
;
(2)求直线
与平面
所成角的余弦值.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdaf03d0342a1b42393d5e41acacc39f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d60dd8220ec310e2bb95d656b1877c2.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959373361152/1572959379636224/STEM/9d6ae5f5c93441ac939c06f0af5049e5.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96cb6d09a254cc2083bffaa10a7c619.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
2016-12-04更新
|
542次组卷
|
7卷引用:2015-2016学年重庆八中高二下第三次周考理科数学试卷
2015-2016学年重庆八中高二下第三次周考理科数学试卷(已下线)2013届湖北省八校高三第二次联考理科数学试卷(已下线)2014届上海交大附中高三数学理总复习二空间向量与立体几何练习卷【全国百强校】贵州省凯里市第一中学2018届高三下学期《黄金卷》第四套模拟考试数学(理)试题广东省汕头市潮阳实验学校2020届高三下学期3月第一次测试理科数学试题上海市浦东新区南汇中学2021-2022学年高二上学期10月月考数学试题(已下线)高二数学上学期【第一次月考卷】(测试范围:第10~11章)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第一册)
10-11高二下·重庆·阶段练习
解题方法
6 . P为正方形ABCD所在平面外一点,PA⊥面ABCD,AE⊥PB,求证:AE⊥PC.
![](https://img.xkw.com/dksih/QBM/2011/4/13/1570117697257472/1570117702549504/STEM/d72d8bd5-3051-4006-a27a-abb7d4c0ef13.png?resizew=177)
您最近一年使用:0次
7 . 如图,在三棱锥
中,
底面
,点
,
分别在棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/57fcf6fd-7399-4ae0-96e5-11f792a852e8.png?resizew=157)
(Ⅰ)求证:
平面
;
(Ⅱ)当
为
的中点时,求
与平面
所成的角的大小;
(Ⅲ)是否存在点
使得二面角
为直二面角?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf87a9d568ef3935c603efcfee863126.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/589c3cc1f331dbb2248b0829039df7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a078495ba47076ccaa28b46f765d80.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/57fcf6fd-7399-4ae0-96e5-11f792a852e8.png?resizew=157)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(Ⅲ)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed479427d768bbf98c15141589109e1.png)
您最近一年使用:0次
2016-11-30更新
|
1836次组卷
|
6卷引用:2010-2011年重庆市完胜田家炳中学高二下学期检测数学试卷
(已下线)2010-2011年重庆市完胜田家炳中学高二下学期检测数学试卷2009年普通高等学校招生全国统一考试理科数学(北京卷)(已下线)2010年大连市第三十六中学高三高考压轴考试理科数学卷(已下线)2012届湖北省岳口中学高三模拟考试理科数学试卷二(已下线)2013届山东省淄川一中高三12月月考理科数学试卷【市级联考】安徽省定远重点中学2018-2019学年高二上学期第三次月考数学(理)试题
8 . 如图,在多面体
中,
平面
,且
是边长为2的等边三角形,
.
是线段
的中点,证明:直线
面
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c5ae16a7145a28a91d45ef950a07c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0968b39e8d3a5146759340413571d0d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69dc003d123423886dba10b28b10b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d3f5f4c4419913c1232b7aae03ade.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db1d8f228c87b65a3609f825fc441d5.png)
您最近一年使用:0次
2016-12-03更新
|
1552次组卷
|
3卷引用:重庆市部分学校2023-2024学年高一下学期5月月考数学试题
9 . 如图4,四边形
为正方形,
平面
,
,
于点
,
,交
于点
.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/728dd7fac41e469ff3e1a1dbe59fb50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f392902d611863c6908a48e696e7bd8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd3699fbb7a8ba3f792cceb24719f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9726261c25e7086835912c0d4815d270.png)
您最近一年使用:0次
2016-12-03更新
|
5399次组卷
|
8卷引用:【全国校级联考】重庆市合川区高2018届高三下5月模拟理科数学试题
【全国校级联考】重庆市合川区高2018届高三下5月模拟理科数学试题2014年全国普通高等学校招生统一考试理科数学(广东卷)2016届宁夏石嘴山三中高三上学期期末考试理科数学试卷陕西省师范大学附属中学2017-2018学年高二上学期期中考试数学(理)试题(已下线)专题24 空间向量与空间角的计算-十年(2011-2020)高考真题数学分项陕西省西安市长安区第一中学2024届高三上学期期中数学(理)试题宁夏石嘴山三中2016届高三(上)期末数学试卷(理科)(解析版)(已下线)专题23 立体几何解答题(理科)-2
13-14高二下·重庆·期中
10 . 如图,四棱锥
中,
,
,
,平面
平面
,
是线段
上一点,
,
.
(1)证明:
⊥平面
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0d476141bdea534f2bd1fd9b5121a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e889baf1905774ce34df07b89bccaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d011620fbbb367d8789faec06c60561f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f7e6fc8324f9f7f826677be25a6479.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449d44b5f2886050e9bc1512be228af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/11c41fd5-7b28-4b52-8360-b906e4188cc9.png?resizew=151)
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