1 . 如图,在四棱锥
中,
,
,
,
,
,
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/4c03f958-7255-40db-8cae-7ca51df324d3.png?resizew=150)
(1)证明:面
平面
.
(2)证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ac6208289b7346c73cde72e01004d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f82a30d6b232dc4d8f35d2d6e0e0f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65334978b0519b379910dfc4acf8344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c2013527c6089d7df59bca21a4598c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/4c03f958-7255-40db-8cae-7ca51df324d3.png?resizew=150)
(1)证明:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8548b4b6a78b672675479fd98a4c8432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b427c2978db0670dc4cb96bffea7e1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
您最近一年使用:0次
2020-03-23更新
|
203次组卷
|
2卷引用:宁夏固原市隆德县2020-2021学年高一上学期期末考试数学试题
名校
解题方法
2 . 如图,直四棱柱
的底面是菱形,
,
,
,
,
,
分别是
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/4c7a6c2c-cecf-4cc3-9d03-464fc44b09ee.png?resizew=159)
(1)证明:
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/4c7a6c2c-cecf-4cc3-9d03-464fc44b09ee.png?resizew=159)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a463a03c549b0dba6d90e7f16a2af.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dc674d6f8169bd48cac0229c18478c.png)
您最近一年使用:0次
2020-03-22更新
|
224次组卷
|
7卷引用:宁夏贺兰县景博中学2020-2021学年高二上学期期末考试数学(理)试题
宁夏贺兰县景博中学2020-2021学年高二上学期期末考试数学(理)试题福建省福清华侨中学2018-2019学年高二下学期期末考试数学(理)试题2020届浙江省杭州市第四中学高三上学期10月月考数学试题广东省江门市棠下中学2022-2023学年高二上学期期中数学试题(已下线)模块四 期中重组篇 专题5 期中重组卷(广东)河北省保定市第一中学2023一2024学年高二上学期第四次阶段考试数学试题(已下线)期中真题必刷易错60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
解题方法
3 . 如图,在四棱锥
中,底面
是菱形,
,且
平面
,
,M,N分别为
,
的中点.
(1)记平面
与底面
的交线为l,试判断直线l与平面
的位置关系,并证明.
(2)点Q在棱
上,若Q到平面
的距离为
,求线段
的长.
![](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/9eee296a7d9fba487f1485c61580196f.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/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/cc23fabd-4b7f-434a-a77c-5cca4797d7e0.png?resizew=155)
(1)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)点Q在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ec70bc9d4f8f5df312e2f09ee3bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
您最近一年使用:0次
名校
4 . 如图,在长方体
中,
,
,点P在棱
上移动.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/3ed0915d-ff2d-4f8a-9b30-e1629787dbb8.png?resizew=231)
(1)证明:
;
(2)
等于何值时,二面角
的大小为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/3ed0915d-ff2d-4f8a-9b30-e1629787dbb8.png?resizew=231)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a028053687dfb26f2f0632f1a5ce1e9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcca9b044ed445b10e2ea3ca8c05f79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,在四棱锥
中,
底面
,
,
,
,
为棱
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/947045a2-452f-4fa1-a310-ffb01af1b3d3.png?resizew=189)
(1)求证:
;
(2)求证:
面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b17e6cbaf17c2ba0a1d333f02aebf58.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/947045a2-452f-4fa1-a310-ffb01af1b3d3.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dac702fe64edf1bc265da4b98cf2a0.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
您最近一年使用:0次
名校
解题方法
6 . 已知四面体ABCD中AB⊥面BCD,BC⊥DC,BE⊥AD垂足为E,F为CD中点,AB=BD=2,CD=1.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d0f01edc-a0d1-4edb-b539-eef19be10057.png?resizew=139)
(1)求证:AC∥面BEF;
(2)求点B到面ACD的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d0f01edc-a0d1-4edb-b539-eef19be10057.png?resizew=139)
(1)求证:AC∥面BEF;
(2)求点B到面ACD的距离.
您最近一年使用:0次
2020-03-18更新
|
652次组卷
|
6卷引用:宁夏回族自治区石嘴山市平罗县平罗中学2019-2020学年高二上学期期末数学(文)试题
名校
解题方法
7 . 已知AB⊥平面ACD,DE⊥平面ACD,△ACD为等边三角形,AD=DE=2AB=2,F为CD的中点.
![](https://img.xkw.com/dksih/QBM/2019/12/21/2362726106701824/2421664816545792/STEM/8c1a48be648e4897a69d1ddc8b3c9904.png?resizew=271)
(1)求证:面BCE⊥面DCE;
(2)求二面角C﹣BE﹣F的余弦值.
![](https://img.xkw.com/dksih/QBM/2019/12/21/2362726106701824/2421664816545792/STEM/8c1a48be648e4897a69d1ddc8b3c9904.png?resizew=271)
(1)求证:面BCE⊥面DCE;
(2)求二面角C﹣BE﹣F的余弦值.
您最近一年使用:0次
名校
8 . 在底面为菱形的四棱柱
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83611e74f5e33dcadf76b217bc7809b.png)
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/0a42a8e2-aba0-4ffd-9398-815efae7fa9a.png?resizew=245)
(1)证明:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ecd4e1a1bb3221c3097e5fe84c11c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83611e74f5e33dcadf76b217bc7809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135c3b8a4e74274de74cf323b819f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/0a42a8e2-aba0-4ffd-9398-815efae7fa9a.png?resizew=245)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5687c7aef5122d5e9c9020af6ea7e6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104bf24922707215be95a860cd533940.png)
您最近一年使用:0次
2020-03-10更新
|
747次组卷
|
9卷引用:宁夏海原县第一中学2021届高三上学期期末考试数学(理)试题
9 . 如图,四棱锥
中,
底面
,
,
,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/2020/3/1/2410295828226048/2411782686670848/STEM/80f55cb9-3869-4c3c-842d-5256a6b9781b.png)
(1)求证:
平面
;
(2)若
,
,
,求四棱锥
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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.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/a763381e4a9e6ac9d9c1df51122570f8.png)
![](https://img.xkw.com/dksih/QBM/2020/3/1/2410295828226048/2411782686670848/STEM/80f55cb9-3869-4c3c-842d-5256a6b9781b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d79e7020414add95907e061df505ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2020-03-03更新
|
360次组卷
|
14卷引用:宁夏平罗中学2020-2021学年高二上学期期末考试数学(文)试题
宁夏平罗中学2020-2021学年高二上学期期末考试数学(文)试题宁夏石嘴山市平罗中学2020-2021学年高二上学期期末数学(文)试题陕西省汉中市2018-2019学年高一下学期期末校际联考数学试题江西省南昌市第十中学2020-2021学年高二上学期期末考试数学(理)试题江西省南昌市第十中学2020-2021学年高二上学期期末考试数学(文)试题新疆新和县实验中学2021-2022学年高一下学期期末考试数学试题宁夏固原市第五中学2022-2023学年高二下学期期中考试数学(文)试题(已下线)【南昌新东方】江西省南昌三中2020-2021学年高二上学期10月第一次月考数学(文)试题云南省弥勒市第一中学2020-2021学年高一下学期第三次月考数学试题江西省宜春市奉新县第一中学2020-2021学年高二下学期第一次月考数学 (理) 试题新疆乌鲁木齐市第八中学2021-2022学年高二上学期第一次月考数学试题江西省赣州市信丰中学2020-2021学年高二下学期入学考试数学(文)试题四川省峨眉第二中学校2022-2023学年高二上学期期中考试文科数学试题云南省昭通市绥江县第一中学2020-2021学年高二上学期第一次月考数学试题
名校
解题方法
10 . 如图所示,在直三棱柱
中,
,
平面
,D为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/9132be8a-cfd6-48e1-8ba1-f9cfc446eb08.png?resizew=166)
(1)求证:
平面
;
(2)求证:
平面
;
(3)设E是
上一点,试确定E的位置使平面
平面BDE,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a9e3a0abf0df191f89169468f95bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/9132be8a-cfd6-48e1-8ba1-f9cfc446eb08.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504a36c231b8e80724d01649e7c0944f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59d296654aa17749f8300ae1d1da0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(3)设E是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
您最近一年使用:0次
2020-03-03更新
|
225次组卷
|
2卷引用:宁夏吴忠市吴忠中学2018-2019学年高一下学期期末数学试题