1 . 如图所示,四棱锥
中,底面
是平行四边形,
平面
,
,
,
是
中点,点
在棱
上移动.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/c919aec0-c857-4408-a3d0-3d9a7778c68b.png?resizew=173)
(1)若
,求证:
;
(2)若
,当点
为
中点时,求
与平面
所成角的大小.
![](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/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/c919aec0-c857-4408-a3d0-3d9a7778c68b.png?resizew=173)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a395778dcf588264f40e1cd8c96206d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e90f9f4e44173888a54c624852064a.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
您最近一年使用:0次
2020-01-04更新
|
493次组卷
|
4卷引用:广东省梅州市大埔县虎山中学2021-2022学年高一下学期5月第二次段考数学试题
广东省梅州市大埔县虎山中学2021-2022学年高一下学期5月第二次段考数学试题(已下线)第8章 立体几何初步 章末综合检测 -2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)(已下线)【新东方】杭州高三数学试卷262浙江省“9+1”高中联盟2019-2020学年高三上学期期中数学试题
2 . 如图所示,已知ABCD是直角梯形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6b28c949-b57a-4359-925b-e65c7bdce20b.png?resizew=174)
(1)证明:
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15fba58c1ecfb2e650da339b7f30d99a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6b28c949-b57a-4359-925b-e65c7bdce20b.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c231fb9aeaf4b73c2d835bb4c3d42b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b183492677d0457b8701c53d9fa1414.png)
您最近一年使用:0次
2019-06-05更新
|
435次组卷
|
3卷引用:广东省揭阳市产业园2019-2020学年高一上学期期末数学试题
3 . 如图所示,
矩形
所在的平面,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2018/2/1/1873186701623296/1874231475232768/STEM/5d7aa3e7e8f8432d9d856fe1e94c128b.png?resizew=185)
(1)求证:
平面
.
(2)
![](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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cca777c664ecc22e40dff4ccae6b248.png)
![](https://img.xkw.com/dksih/QBM/2018/2/1/1873186701623296/1874231475232768/STEM/5d7aa3e7e8f8432d9d856fe1e94c128b.png?resizew=185)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab384f2520d76ed8fa01b31e09c1eea.png)
您最近一年使用:0次
2018-02-03更新
|
996次组卷
|
12卷引用:广东省揭阳市第三中学2017-2018学年高一上学期期末考试数学试题
广东省揭阳市第三中学2017-2018学年高一上学期期末考试数学试题(已下线)2011-2012年河南省许昌市高一上学期期末测试数学(已下线)2011-2012学年山东省梁山二中高一12月份月考数学试卷2015-2016学年福建省上杭一中高一上第二次月考数学试卷江苏省镇江中学2020-2021学年高一下学期期末数学试题湖北省武汉市第四十九中2020-2021学年高一下学期5月月考数学试题(已下线)第11练 空间直线、平面的平行-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)江苏省南京师范大学附属中学秦淮科技高中2022-2023学年高一下学期5月月考数学试题江苏省镇江第一中学、大港中学等八校2022-2023学年高一下学期5月月考数学试题江苏省南京市人民中学、海安市实验中学、句容市第三中学、镇江心湖高级中学2022-2023学年高一下学期5月学情调研数学试题2015-2016学年河北省邢台市二中高二上第一次月考数学试卷2016-2017学年河北省卓越联盟高二上学期月考一数学试卷
4 . 如图所示,在直三棱柱
中,
,
,
、
分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/a360770cad0049318dc29dfdcee604cd.png)
(Ⅰ)求证:
;
(Ⅱ)求证:
.
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/fbef4db8d5aa423cbacb95006f89ae1e.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/50ecfc2a16a04fabba73e5b1af347b32.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/e7623c64bc4b41159bfe1cdfffdafbaf.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/5e052a2152af4d8bbecfe31c6b2aec84.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/ece7110146a040c6a825b421209f8244.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/bdf323d2e36649dabaf6e39394969b03.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/5627290e743141d89541ec5af569e78b.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/a360770cad0049318dc29dfdcee604cd.png)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/a44ac4711047478eae32b5ade1ca7f06.png)
(Ⅱ)求证:
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/ffb18a06fe65498f9409b0a42500bab6.png)
您最近一年使用:0次
5 . 如图,三棱柱ABC﹣A1B1C1中,AA1⊥BC,A1B⊥BB1,
(2)若AB=2,AC=,BC=
,问AA1为何值时,三棱柱ABC﹣A1B1C1体积最大,并求此最大值.
您最近一年使用:0次
2016-12-12更新
|
3393次组卷
|
7卷引用:广东省潮州市2021-2022学年高一下学期期末数学试题
广东省潮州市2021-2022学年高一下学期期末数学试题湖南师范大学附属中学2021-2022学年高一下学期第二次月考数学试题(已下线)期末复习07 空间几何线面、面面垂直-期末专项复习2014年全国普通高等学校招生统一考试文科数学(江西卷)安徽省合肥一中2020-2021学年高二上学期10月段考数学(理)试题江西省八校(新余一中、宜春中学等)2020-2021学年高二下学期第四次联考数学(文)试题(已下线)专题23 立体几何解答题(文科)-3
6 . 如图,在直三棱柱ABC﹣A1B1C1中,AC⊥BC,点D是AB的中点.求证:
![](https://img.xkw.com/dksih/QBM/2016/4/13/1572592678387712/1572592684408832/STEM/b36a2c5f71ba4bb5b8e12a321e3698b1.png)
(1)AC⊥BC1;
(2)AC1∥平面B1CD.
![](https://img.xkw.com/dksih/QBM/2016/4/13/1572592678387712/1572592684408832/STEM/b36a2c5f71ba4bb5b8e12a321e3698b1.png)
(1)AC⊥BC1;
(2)AC1∥平面B1CD.
您最近一年使用:0次
2016-12-04更新
|
565次组卷
|
2卷引用:【市级联考】广东省湛江市2017-2018学年高一上学期期末考试数学试题
7 . 如图,正四棱锥
的底面是边长为
的正方形,侧棱长是底面边长为
倍,
为底面对角线的交点,
为侧棱
上的点.
![](https://img.xkw.com/dksih/QBM/2015/8/25/1572220230975488/1572220236660736/STEM/7d70172218c543c58c58ac6a6b031c7d.png)
(1)求证:
;
(2)
为
的中点,若
平面
,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aa0d36da718de7c50a781b8e2bb8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://img.xkw.com/dksih/QBM/2015/8/25/1572220230975488/1572220236660736/STEM/7d70172218c543c58c58ac6a6b031c7d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d785b183d9b7ddf4f9f60ca49a2fc3ba.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab3cc5d6891b01c98e1429da8a58d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
8 . 如图,正方形
的边长为1,正方形
所在平面与平面
互相垂直,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/40a599c4-e52f-44e3-bef3-3607dd994c7d.png)
(1)求证:
平面
;
(2)求证:
;
(3)求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/cd4593287214468b9f5343d3148070c5.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/870bff5fc0584b4ea927c9c25db8d8a1.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/cd4593287214468b9f5343d3148070c5.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/bac69173fe9b402c8e6f3db24d2007ea.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/7e437572ab474dc8b91ab683b65adcc4.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/40a599c4-e52f-44e3-bef3-3607dd994c7d.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/4e37268c2f884d7f86ba1510c3ef3a7d.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/a1ac04b2cf04497caf3c34b08f69eacb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc4c50ada59b5838d296697a8e0bb8d.png)
(3)求三棱锥
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/fcfaed65b36041d9bd03ff656a6b3760.png)
您最近一年使用:0次
9 . 如图,正方体
的棱长为
,
分别为
的中点.
(1)求证:
;
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d52429789f22fe9061973e123a038d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f5572d9521e112be8148fea4d7241f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16155b0c208b346e93529385c8793b49.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74534a54d7271e1b95fd3a74121468b.png)
![](https://img.xkw.com/dksih/QBM/2017/2/16/1625334186016768/1632305636458496/STEM/3ef8953362d0463789f94b1d9d73efde.png?resizew=218)
您最近一年使用:0次
2017-02-26更新
|
473次组卷
|
2卷引用:2016-2017学年广东省珠海市高一上学期期末考试B数学试卷
10 . 在正三棱锥
中,
、
分别为棱
、
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/2ba52750b4c54f94a53a9e5ead3d1cd2.png)
(1)求证:直线
平面
;
(2)求证:平面
平面
.
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/06a1a2bd819a44c982a525ad6cde88df.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/31e6e0f27e9e48be86cebe33864a9223.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/41469a49c14b4de586c547ff8df8bc98.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/940335b942964da888138fc6690f4f5a.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/960ff362f8da4645bd3dcf59ad26abee.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/b106e917b59340c384ebd38015c24826.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/2ba52750b4c54f94a53a9e5ead3d1cd2.png)
(1)求证:直线
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/f38c6affd7034c46b6e7384380ce8c91.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/34c371fb18144b0ba07dda89b61665c3.png)
(2)求证:平面
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/0721aeca5f464bd3ac7c553fde9eb777.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/f29f0ced562b4449b8ecd08a228540fe.png)
您最近一年使用:0次