名校
解题方法
1 . 如图,四棱柱
中,
底面
,四边形
为梯形,
,且
,
为
的中点,过
三点的平面记为
.
(Ⅰ)证明:平面
与平面
的交线平行于直线
;
![](https://img.xkw.com/dksih/QBM/2017/5/17/1688962389204992/1689505977835520/STEM/749982a9-901d-4edd-9011-ad2c9f13f56a.png?resizew=176)
(Ⅱ)若
,
,求平面
与底面
所成二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.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/e839ac941e8bf536ff35a12e56c7a400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58686e417f5d9cbfa8ef97e180af9f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(Ⅰ)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2017/5/17/1688962389204992/1689505977835520/STEM/749982a9-901d-4edd-9011-ad2c9f13f56a.png?resizew=176)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604ea9581e49ea3531d5f82349e61553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9f9fcdffb61b5366a158ebd115cd3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2017-05-18更新
|
908次组卷
|
7卷引用:江西省景德镇一中2022-2023学年高一(18班)下学期期中考试数学试题
2 . 如图,三棱锥
中,
平面
,
,
,
是
的中点,
是
的中点,点
在
上,
.
![](https://img.xkw.com/dksih/QBM/2017/2/16/1625395186098176/1635395675070464/STEM/5a7ebc730fc54d89b51a38bd4820cc6e.png?resizew=178)
(1)证明:
平面
;
(2)若
,求二面角
的余弦值.
![](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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bae7599ad243c12d94325ad917f0a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51627b773b078f4b3651e4459e547da6.png)
![](https://img.xkw.com/dksih/QBM/2017/2/16/1625395186098176/1635395675070464/STEM/5a7ebc730fc54d89b51a38bd4820cc6e.png?resizew=178)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ca12f11f39405a6a49042c5e294862.png)
您最近一年使用:0次
2017-03-02更新
|
2992次组卷
|
2卷引用:湖南省长沙市明德中学2019-2020学年高二上学期期中数学试题
名校
解题方法
3 . 如图所示,
为平行四边形
所在平面外一点,
分别为
的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2017/5/10/1684074014965760/1689882530930688/STEM/97509fd7274645bfbea343df3711917d.png?resizew=225)
(1)判断
与
的位置关系,并证明你的结论;
(2)判断
与平面
的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbb19cb4eb2d7f3207559eb07355ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c659d2ab07b9b66ed9a60cb604dd9aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e61111c1e9b98b79615f75540175c9.png)
![](https://img.xkw.com/dksih/QBM/2017/5/10/1684074014965760/1689882530930688/STEM/97509fd7274645bfbea343df3711917d.png?resizew=225)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2017-05-18更新
|
546次组卷
|
2卷引用:河北省张家口市第一中学2016-2017学年高一下学期期中考试(衔接班)数学(理)试题
名校
解题方法
4 . 在直三棱柱
中,
,延长
到
,使
,连结
,得到多面体
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/18/c0649f53-6fe9-4239-8690-7a9b86cb856b.png?resizew=240)
(1)证明:
平面
;
(2)若
,
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ddd49625097d0a78df7170be4f882e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa265e6bf764ba99120bf8858fc29cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b1dd0fbfc62602b496a1ddce721d94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/18/c0649f53-6fe9-4239-8690-7a9b86cb856b.png?resizew=240)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504a36c231b8e80724d01649e7c0944f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3d1518e197f7f25c341da6b1e3483.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58899f5c3638f1e32274137723f99836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b1dd0fbfc62602b496a1ddce721d94.png)
您最近一年使用:0次
2017-06-18更新
|
726次组卷
|
2卷引用:江西省南昌市第十中学2022-2023学年高二上学期期中数学试题
解题方法
5 . 如图,三棱锥
中,
⊥底面
,
,
,
为
的中点,
为
的中点,点
在
上,且
.
![](https://img.xkw.com/dksih/QBM/2016/1/15/1572437735358464/1572437741314048/STEM/86b747fb97d94f2f9b74cb15f70d645a.png?resizew=132)
(1)求证:
⊥平面
;
(2)求证:
∥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3cc9cccfb4c260dac05f4ed57e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a722f046ce210dce133cf61b130c7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a41ada2c69a8c4ff1c0a9c780d2a08d.png)
![](https://img.xkw.com/dksih/QBM/2016/1/15/1572437735358464/1572437741314048/STEM/86b747fb97d94f2f9b74cb15f70d645a.png?resizew=132)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
真题
名校
6 . 在如图所示的圆台中,AC是下底面圆O的直径,EF是上底面圆O
的直径,FB是圆台的一条母线.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/3/f0218997-2f80-43b2-8240-e0f8c27d5e25.png?resizew=200)
(Ⅰ)已知G,H分别为EC,FB的中点,求证:GH∥平面ABC;
(Ⅱ)已知EF=FB=
AC=
,AB=BC.求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9041a3dc5017c192cad54b40aa3f35f9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/3/f0218997-2f80-43b2-8240-e0f8c27d5e25.png?resizew=200)
(Ⅰ)已知G,H分别为EC,FB的中点,求证:GH∥平面ABC;
(Ⅱ)已知EF=FB=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47342449ca1a78a7550975a7589003c5.png)
您最近一年使用:0次
2016-12-04更新
|
2111次组卷
|
11卷引用:2016-2017学年河北定州市高二上学期期中数学试卷
2016-2017学年河北定州市高二上学期期中数学试卷2016年全国普通高等学校招生统一考试理科数学(山东卷精编版)人教A版高中数学必修二 2.3.2 平面与平面垂直的判定(已下线)专题17 立体几何综合-五年(2016-2020)高考数学(理)真题分项湖北省黄冈中学2021届高三下学期5月适应性考试数学试题河北正定中学2021届高三上学期第四次半月考数学试题沪教版(2020) 一轮复习 堂堂清 第八单元 8.10 空间向量在立体几何中的应用(二)(已下线)2016年全国普通高等学校招生统一考试理科数学(山东卷参考版)(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(已下线)专题23 立体几何解答题(理科)-1专题31立体几何与空间向量解答题(第二部分)
解题方法
7 . 如图,在三棱锥
中,平面
平面
,
为等边三角形,
,且
,O,M分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2016/2/23/1572493459259392/1572493465501696/STEM/e112da64-89cf-47ca-8c60-0f038e0e7958.png?resizew=273)
(Ⅰ)求证:
平面
;
(Ⅱ)设
是线段
上一点,满足平面
平面
,试说明点的位置
;
(Ⅲ)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8704811c9c5dba854310ae0de2ba6b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f63075fdeeb9e765dd696c4ff43ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bc7774144c164f7ebaeca54fa657e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://img.xkw.com/dksih/QBM/2016/2/23/1572493459259392/1572493465501696/STEM/e112da64-89cf-47ca-8c60-0f038e0e7958.png?resizew=273)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a56d04dee1d94bb694c34706ee0af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08452588675f76da2f8d31387b3a8224.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe4f0e847eee390f76f04bb4cf53b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af57d63e83ef0e183add10cd6beec65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(Ⅲ)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
您最近一年使用:0次
2016-12-04更新
|
857次组卷
|
2卷引用:2015-2016学年天津市一中高二上学期期中理科数学试卷
名校
解题方法
8 . 在正方体
中.
![](https://img.xkw.com/dksih/QBM/2019/6/7/2220499513712640/2221089699241984/STEM/d64269675fca4533a7deea17e368ce25.png?resizew=154)
(1)若
为棱
上的点,试确定点
的位置,使平面
;
(2)若
为
上的一动点,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cf99a0d5833beacc3a0ee39d39458.png)
![](https://img.xkw.com/dksih/QBM/2019/6/7/2220499513712640/2221089699241984/STEM/d64269675fca4533a7deea17e368ce25.png?resizew=154)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4ee628f1f5b2c224e4e9a759ffc305.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349740b9aa8c242258eb07cb7224c3f6.png)
您最近一年使用:0次
2016-12-03更新
|
817次组卷
|
2卷引用:新疆乌鲁木齐市第七十中学2018-2019学年高一下学期期中考试数学(理)试题
12-13高一上·北京·期末
解题方法
9 . 在四棱锥
中,底面
是直角梯形,
,
,
,平面
平面
.
(1)求证:
平面
;
(2)求平面
和平面
所成二面角(小于
)的大小;
(3)在棱
上是否存在点
使得
平面
?若存在,求
的值;若不存在,请说明理由.
![](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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0073c8e806d0399a6983e163f0fd176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ba22238cdff318a4bd9d4d746b3229.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5865d488a9cf1181016fd2e866177cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b505e0df1131e3a93fc81d13f6e224e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/fa4fd412-897c-4621-b148-dc248d6cc7a6.png?resizew=135)
您最近一年使用:0次
2016-12-02更新
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651次组卷
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5卷引用:北京西城回民中学2018届高三上期中数学(理)试题
北京西城回民中学2018届高三上期中数学(理)试题北京市东城区2018届高三上学期期中考试数学试题(已下线)2011-2012学年北京市育园中学高一第一学期期末考试数学(已下线)2011-2012学年北京市海淀区高三上学期期末考试理科数学(已下线)2013届天津市天津一中高三第三次月考理科数学试卷