解题方法
1 . 如图所示,在直棱柱
中,底面
是直角梯形,
.
![](https://img.xkw.com/dksih/QBM/2017/1/18/1619460899946496/1619460900560896/STEM/46b0571aa0e64d7daa9e2816626e11d7.png?resizew=204)
(1)求证:平面
平面
;
(2)在
上是否存在一点
,使得
与平面
和平面
都平行?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e8b29d8231fdf1e58a40da4ca7e7e5.png)
![](https://img.xkw.com/dksih/QBM/2017/1/18/1619460899946496/1619460900560896/STEM/46b0571aa0e64d7daa9e2816626e11d7.png?resizew=204)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803fa75db3ac3a26a41e347dc4165026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
您最近一年使用:0次
12-13高一·福建泉州·假期作业
名校
解题方法
2 . 如图,在四棱锥
中,
底面ABCD,
,
,
,PA=AB=BC,E是PC的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/4d07cfb4-486f-4606-802c-bb4baaa264dd.png?resizew=160)
(1)
;
(2)
平面ABE.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/4d07cfb4-486f-4606-802c-bb4baaa264dd.png?resizew=160)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dac702fe64edf1bc265da4b98cf2a0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
您最近一年使用:0次
2022-09-18更新
|
1570次组卷
|
35卷引用:2016-2017学年陕西西安中学高一上学期质检三数学试卷
2016-2017学年陕西西安中学高一上学期质检三数学试卷天津市红桥区2017-2018学年高二上学期期中考试数学(文)试题人教A版高中数学必修二 2.3.1直线与平面垂直的判定2人教A版高中数学必修二 2.3.3 直线与平面垂直的性质2山西省朔州市应县第一中学校2019-2020学年高二上学期第一次月考数学(理)试题安徽省滁州市定远县育才学校2020-2021学年高二上学期第二次月考数学(文)试题江西省赣州市南康中学2020-2021学年高二上学期第四次大考数学(文)试题云南省弥勒市第一中学2020-2021学年高二下学期第三次月考数学(文)试题江苏省常州市武进区礼嘉中学2020-2021学年高一下学期第二次阶段质量调研数学试题天津市静海区独流中学2021-2022学年高二上学期10月月考数学试题河南省新乡市第十一中学2020-2021学年高二下学期第二次月考文科数学试题陕西省延安中学2022-2023学年高一下学期期中数学试题(已下线)2012-2013学年福建省南安一中高一寒假作业1数学试卷(已下线)2013届辽宁省五校协作体高三摸底考试文科数学试卷2015-2016学年安徽省阜阳市太和县二职高一上学期期末数学试卷(已下线)2019年11月17日 《每日一题》必修2-每周一测人教A版(2019) 必修第二册 过关斩将(高手篇) 第八章 8.6 空间直线、平面的垂直人教B版(2019) 必修第四册 过关斩将(高手篇) 第十一章 立体几何初步 11.4 空间中的垂直关系人教A版(2019) 必修第二册 突围者 第八章 第六节 课时2 直线与平面垂直江苏省苏州市外国语学校2018-2019学年高二下学期期中数学(文)试题(已下线)【新教材精创】11.4.1直线与平面垂直(第2课时)练习(1)云南省大理州祥云县2019-2020学年高二下学期期末统测数学(文)试题吉林省长春市第二十九中学2020-2021学年高一下学期期中数学试题(已下线)课时1.1.2 空间向量及其运算(02)空间向量的数量积运算-2021-2022学年高二数学同步练习和分类专题教案(人教A版2019选择性必修第一册)(已下线)考点48 直线与平面、平面与平面垂直-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】(已下线)第37讲 立体几何中的向量方法 (讲) — 2022年高考数学一轮复习讲练测(课标全国版)人教A版(2019) 必修第二册 实战演练 第八章 课时练习30 直线与平面垂直空间向量及其运算(已下线)第48讲 直线与平面、平面与平面垂直人教A版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 1.1 空间向量及其运算 1.1.2 空间向量的数量积运算(已下线)8.6.2直线与平面垂直的性质定理(第2课时)(精讲)(1)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)重点题型训练13:第6章平行关系、垂直关系-2020-2021学年北师大版(2019)高中数学必修第二册(已下线)专题训练:线线、线面、面面垂直证明第3章 空间向量与立体几何测试题 -2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册(已下线)艺体生一轮复习 第七章 立体几何 第34讲 空间中的垂直关系【讲】
名校
3 . 如图,在三棱锥
中,底面
是边长为4的正三角形,
,侧面
垂直于底面
,
、
分别是
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/e9130ce0-aee0-4ec9-ade3-30dae57ea060.png?resizew=185)
(1)求证:
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab430bcf8a8961dbb3c3ef7ccd8f875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/e9130ce0-aee0-4ec9-ade3-30dae57ea060.png?resizew=185)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd0b96e493a050ceafbb499c178f6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
4 . 在如图所示的几何体中,四边形
为正方形,四边形
为等腰梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/45b8ed1e-cc65-4da6-9f0a-465ff76ee505.png?resizew=172)
(1)求证:
平面
;
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.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/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526908dfb46cf151b8ab1492a9d52047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5867254f6e74a3e31237279cd481f6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/45b8ed1e-cc65-4da6-9f0a-465ff76ee505.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e51817ee1ebf17c73ed21171bcfc5b5.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6e3f0518632294dc748ca9710d15b7.png)
您最近一年使用:0次
2020-01-28更新
|
358次组卷
|
2卷引用:2018届陕西省西安中学高三上学期第一次摸底考试数学(文)试题
5 . 如图所示,空间四边形ABCD中,E,F,G,H分别是AB,BC,CD,DA上的点,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39448a03e5af689640e7a643e4a9f80c.png)
![](https://img.xkw.com/dksih/QBM/2019/2/2/2131869402423296/2137469848272896/STEM/12f36b632c734b6ca546b3340345f8ba.png?resizew=114)
(1)求证:四边形EFGH是梯形;
(2)若BD=a,求梯形EFGH的中位线的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39448a03e5af689640e7a643e4a9f80c.png)
![](https://img.xkw.com/dksih/QBM/2019/2/2/2131869402423296/2137469848272896/STEM/12f36b632c734b6ca546b3340345f8ba.png?resizew=114)
(1)求证:四边形EFGH是梯形;
(2)若BD=a,求梯形EFGH的中位线的长.
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,
面
,
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2017/12/14/1838106529947648/1838350908178432/STEM/c77f29e937414c44b7ceca6ddbf76bbe.png?resizew=152)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/9f14fe22376f70a50752d3e146b8e1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c05bbc5dbc0cd9ba0414ee79f501db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2017/12/14/1838106529947648/1838350908178432/STEM/c77f29e937414c44b7ceca6ddbf76bbe.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b38bc08d7904222164fe46926abda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4fa4b484441ff4c95b2b757e6222ea.png)
您最近一年使用:0次
2017-12-14更新
|
671次组卷
|
3卷引用:陕西省西安中学2018届高三10月月考数学(文)试题
名校
解题方法
7 . 如图,在三棱锥
中,
,
,侧面
为等边三角形,侧棱
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/4/4b0dcdec-5b27-47e7-b635-1e47ed54b2df.png?resizew=168)
(1)求证:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ced8225ff27c8e3e1897b8629312d5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/4/4b0dcdec-5b27-47e7-b635-1e47ed54b2df.png?resizew=168)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e820aec9c1a975242fe6d76408a9cde8.png)
您最近一年使用:0次
2017-12-14更新
|
486次组卷
|
4卷引用:陕西省西安中学2018届高三10月月考数学(理)试题
解题方法
8 . 如图,多面体
中,四边形
为矩形,
,
,且
,
,
分别为
,
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/14/63353b4e-7002-43b2-8973-40d551dd2dec.png?resizew=175)
(1)若三棱锥
的体积为
,求
的长;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5c816b8b83b9d7cfd260fadded614f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6933009c0119b0f380e303b5ef862d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae368b7b43ff9b6cdbed1709ebee583e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/14/63353b4e-7002-43b2-8973-40d551dd2dec.png?resizew=175)
(1)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab49dbd84db02bf3313dfdf1ca1cc74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77230906b2c3d4851a0b1b8a705cd1b7.png)
您最近一年使用:0次
名校
解题方法
9 . 如图:等边三角形
所在的平面与
所在的平面互相垂直,
分别为
边中点.已知
,
,
.
![](https://img.xkw.com/dksih/QBM/2017/11/17/1819247073312768/1821503961874432/STEM/227a2eff03594eab838588ec5b23536b.png?resizew=227)
(1)证明:
平面
;
(2)证明:
;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc8af7ee9dcd84ec714c3e87b8b3959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.png)
![](https://img.xkw.com/dksih/QBM/2017/11/17/1819247073312768/1821503961874432/STEM/227a2eff03594eab838588ec5b23536b.png?resizew=227)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f45265eaed2ba5fc08f6a112a02cd2.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
您最近一年使用:0次
10 . 如图,在四棱锥
中,底面
为直角梯形,且
,
,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
底面
,
为
的中点,
是棱
的中点,.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f4b8bfd986ef94263a381b6caba5c9.png)
(1)求证:
平面
;
(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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ff6d7dd48b57f03d82d2c522ee9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f4b8bfd986ef94263a381b6caba5c9.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f79db7c270b6ff9fb0a538ee201cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76f6552e20faeba98588e9b5dd01f6e.png)
![](https://img.xkw.com/dksih/QBM/2017/4/17/1667898005307392/1668235543429120/STEM/a2699919c58541c68dfdafdaebc2825a.png?resizew=201)
您最近一年使用:0次
2017-04-18更新
|
674次组卷
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3卷引用:2017届陕西省黄陵中学高三(重点班)4月月考(高考全国统一全真模拟二)数学(文)试卷