名校
解题方法
1 . 如图,在四边形
中,
,以
为折痕把
折起,使点
到达点
的位置,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/c29e0c78-6351-4c42-9580-dc889bc1491c.png?resizew=141)
(1)证明:
平面
;
(2)若
为
的中点,二面角
等于60°,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aad2d7c7a8177255f745b3b8101b7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307d38cc7012c328f1f22aa793fe76d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/c29e0c78-6351-4c42-9580-dc889bc1491c.png?resizew=141)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f35614aff055b98b76ca262f64e629d.png)
您最近一年使用:0次
2020-05-12更新
|
1706次组卷
|
8卷引用:2020届山东省聊城市高三高考模拟(一)数学试题
解题方法
2 . 如图,在三棱柱
中,侧面
底面
,
,
,
分别是棱
,
的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/a918df66-bc78-4c8e-9c3a-6c2d3bc4cc8d.png?resizew=155)
(1)
∥平面
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/a918df66-bc78-4c8e-9c3a-6c2d3bc4cc8d.png?resizew=155)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b6c68ad9b2e22725f3cbf7c1a3f8dc.png)
您最近一年使用:0次
2020-05-01更新
|
738次组卷
|
6卷引用:2020届江苏省南通市基地学校高三下学期第二次大联考数学试题
2020届江苏省南通市基地学校高三下学期第二次大联考数学试题江苏省徐州市2020届高三下学期考前模拟(四模)数学试题(已下线)专题15 空间线面位置关系的证明-2020年高考数学母题题源解密(江苏专版)江苏省徐州市2020届高三(6月份)高考数学考前模拟试题江苏省扬州市高邮市第一中学2020-2021学年高三上学期10月测试数学试题云南省云南师范大学附属镇雄中学2022-2023学年高一下学期5月月考数学试题
名校
解题方法
3 . 如图,已知矩形
和直角梯形
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/55180bcc-5a64-44c7-94b5-517e846b2fc8.png?resizew=186)
(1)求证:
平面
;
(2)求证:
.
![](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/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ff6d7dd48b57f03d82d2c522ee9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518586d91b63569fc317b323835a0c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/55180bcc-5a64-44c7-94b5-517e846b2fc8.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8197bf06d017950c85c3ba6a291c095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66058ff40f4ebfc19490eb4e20360752.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991e1a8f2b85baab1fe2c4d3b49ecf9b.png)
您最近一年使用:0次
2020-03-26更新
|
680次组卷
|
4卷引用:2020届江苏省南京一中高三上学期期中数学试题
解题方法
4 . 如图,空间几何体
中,四边形
,
是全等的矩形,平面
平面
,且
,
,
,
分别为线段
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/a0d2115d-7846-45ae-a035-fc3b91779a58.png?resizew=109)
(1)求证:
平面
;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a68a008a22d5a8cea5fe8dcf31e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/a0d2115d-7846-45ae-a035-fc3b91779a58.png?resizew=109)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec0d564163fc8886ffacac55ca49e2d.png)
您最近一年使用:0次
名校
5 . 如图,四棱锥P﹣ABCD的底面是梯形.BC∥AD,AB=BC=CD=1,AD=2,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8f9efada515904b015baa8e2fc1b8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/bd80ff47-3d74-46af-9200-fe32847a61d5.png?resizew=177)
(Ⅰ)证明;AC⊥BP;
(Ⅱ)求直线AD与平面APC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96ac79190e1b93c16b5d00a1b516281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8f9efada515904b015baa8e2fc1b8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/bd80ff47-3d74-46af-9200-fe32847a61d5.png?resizew=177)
(Ⅰ)证明;AC⊥BP;
(Ⅱ)求直线AD与平面APC所成角的正弦值.
您最近一年使用:0次
2020-03-22更新
|
930次组卷
|
7卷引用:2020届浙江省杭州二中高三上学期返校考试数学试题
2020届浙江省杭州二中高三上学期返校考试数学试题2020届浙江省温州中学高三下学期3月高考模拟测试数学试题福建省三明市2019-2020学年普通高中高三毕业班质量检查A卷(5月联考)理科数学试题福建省三明市2019-2020学年高三(5月份)高考(理科)数学模拟试题(已下线)考点23 运用空间向量解决立体几何问题-2021年高考数学三年真题与两年模拟考点分类解读(新高考地区专用)(已下线)专题19 立体几何综合-2020年高考数学母题题源全揭秘(浙江专版)安徽省滁州市定远县第二中学2022届高三下学期高考模拟检测理科数学试题
名校
解题方法
6 . 已知三棱柱
的底面是正三角形,侧面
为菱形,且
,平面
平面
,
、
分别是
、
的中点.
![](https://img.xkw.com/dksih/QBM/2020/3/19/2423138566766592/2423630358208512/STEM/05a2608adae7431da5b603bf448c3633.png?resizew=217)
(1)求证:
平面
;
(2)求证:
;
(3)求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2020/3/19/2423138566766592/2423630358208512/STEM/05a2608adae7431da5b603bf448c3633.png?resizew=217)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb9aa113258bfa138c95a621f64fc74.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
您最近一年使用:0次
2020-03-20更新
|
664次组卷
|
4卷引用:【全国百强校】天津市静海县第一中学2017-2018学年高一下学期期中考试数学试题
名校
解题方法
7 . 如图,在三棱锥
中,
平面
,
,
分别为棱
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/c086d471-6389-479b-9c2a-5fb8e02b812e.png?resizew=196)
(1)求证:
;
(2)当
时,求三棱锥
的表面积.
![](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/c46cf65da6cf1a1a7fc5c9c01bdd83a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6476880c8c4a6a9c1883d6fbb42cd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534c25b4b9ff9aa0cf6c05ae3a8f02f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/c086d471-6389-479b-9c2a-5fb8e02b812e.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01071e7ea0fe51f5d9912c27343db0ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2020-03-20更新
|
210次组卷
|
2卷引用:2020届安徽省安庆二、七中高三开学考试数学(理)试题
8 . 如图,四棱锥
的底面是矩形,
,且
底面
.
![](https://img.xkw.com/dksih/QBM/2020/3/17/2421383968727040/2422388324564992/STEM/7e93bf53-7fa3-4639-aae6-93b8d899c4c2.png)
(1)求向量
在向量
上的投影;
(2)若线段
上存在异于
的一点
,使得
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e43f5f5c26f0b7315d8241445f4cd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2020/3/17/2421383968727040/2422388324564992/STEM/7e93bf53-7fa3-4639-aae6-93b8d899c4c2.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4709f45dc9e6f3f7d7727e54cf481d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054fbd8b89b8e78589db1312573da97a.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ba0ddcffcbc270daef181d99886907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-03-18更新
|
373次组卷
|
3卷引用:陕西省西安中学2017-2018学年高二(平行班)上学期期中数学(理)试题
陕西省西安中学2017-2018学年高二(平行班)上学期期中数学(理)试题(已下线)[新教材精创] 1.1 空间向量其运算(提高练习) -人教A版高中数学选择性必修第一册甘肃省武威市等2地2022-2023学年高二上学期期中联考理科数学试题
名校
9 . 如图①所示,四边形
为等腰梯形,
,且
于点
为
的中点.将
沿着
折起至
的位置,使得平面
平面
,得到如图②所示的四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/af2fd598-ef45-4147-b869-0285bfcbd60f.png?resizew=437)
(1)求证:
;
(2)求平面
与平面
所成的锐二面角的余弦值.
![](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/247e96a3a378741eb42dda3837ea5c7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3814287dbb60d478bffc5366f9928b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353732838789714499619085201305c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33719580ce50fafc3a27eb7039be8a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/decee6072217173778edc84db382f97b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/af2fd598-ef45-4147-b869-0285bfcbd60f.png?resizew=437)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c723ad583a4009b7a5dd515e7e02b8a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7f857869bc6084d128e8c13f5c115c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
您最近一年使用:0次
解题方法
10 . 如图,EB垂直于菱形ABCD所在平面,且EB=BC=2,∠BAD=60°,点G、H分别为线段CD、DA的中点,M为BE上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/f4134a83-f2d8-48a2-a19a-b58415b15228.png?resizew=206)
(Ⅰ)求证:GH⊥DM;
(Ⅱ)当三棱锥D﹣MGH的体积最大时,求三角形MGH的面积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/f4134a83-f2d8-48a2-a19a-b58415b15228.png?resizew=206)
(Ⅰ)求证:GH⊥DM;
(Ⅱ)当三棱锥D﹣MGH的体积最大时,求三角形MGH的面积.
您最近一年使用:0次