名校
1 . 如图,平行六面体
中,底面
是边长为2的正方形,
为
与
的交点,
.
平面
;
(2)求二面角
的正弦值.
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5507b438b67e02fe40f8b0beb6f585f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ad2917b716db41c03e670f77d411d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104bf24922707215be95a860cd533940.png)
您最近一年使用:0次
2024-01-19更新
|
7494次组卷
|
9卷引用:2024年九省联考试卷分析及真题鉴赏
2024年九省联考试卷分析及真题鉴赏2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19(已下线)专题05 空间向量与立体几何(分层练)(四大题型+21道精选真题)(已下线)微考点5-1 新高考新试卷结构立体几何解答题中的斜体建坐标系问题(已下线)专题6-3立体几何大题综合归类-2湖北省部分学校2023-2024学年高二上学期期末数学试题广东省中山市中山纪念中学2024届高三下学期开学模拟测试数学试题(一)福建省厦门双十中学2023-2024学年高二下学期开学考试数学试题
2 . 将边长为2的等边
沿
边中线
折起得到三棱锥
,当所得三棱锥体积最大时,点
到平面
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
3 . 如图,
为圆锥的顶点,
为底面圆心,点
,
在底面圆周上,且
,点
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5ef9d746-ef49-4c37-be9e-98f2ad103e02.png?resizew=125)
(1)求证:
;
(2)若圆锥的底面半径为2,高为4,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5ef9d746-ef49-4c37-be9e-98f2ad103e02.png?resizew=125)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464e16e3387532eb66521b4e97791cae.png)
(2)若圆锥的底面半径为2,高为4,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fa483ce5e3575ff399722caba7b943.png)
您最近一年使用:0次
4 . 如图,在四棱锥
中,平面
平面
,四边形
为正方形,
为等边三角形,点
在
上,
,点
为线段
的中点,点O为三角形
的重心.
(1)求证:
平面
;
(2)若四棱锥
的体积为
,求四棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905f4cbe939c528692f367fe34333216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b265d121f9ebc13671a5719604476a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/cb3d1c8d-94a1-45da-8d4c-33ebc434c20e.png?resizew=115)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc36cda92e01d6f85e9e2e6c0917ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2278dbf1ada5dc5289063e5f77c22b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
您最近一年使用:0次
5 . 如图,在四棱锥
的平面展开图中,底面
为等腰梯形,
,
,
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2dcbd21a3520114a8349c838136579.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def26b3c1c08356f8fa49c85fe19476b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ea9d92e5c258a50af1e461c7388894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db27b7f29d7d01b2692f217bc3079fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5de1f13f61b328b64413025273f1580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2dcbd21a3520114a8349c838136579.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/1a3716fd-ef84-4ed7-aa99-48a14a504cfc.png?resizew=136)
您最近一年使用:0次
解题方法
6 . 如图,在四棱锥
中,底面
是矩形,平面
⊥平面
,
为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/aa208230-f1d8-4e11-8ea4-37f5ac0a338f.png?resizew=158)
(1)求证:平面
⊥平面
;
(2)求二面角
的余弦值.
![](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/1e582d73b96ba649378379c3074d506d.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b8e42d656d2da9ecf96ac60b6f99c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db86a481972bd2dc553889617002d146.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/aa208230-f1d8-4e11-8ea4-37f5ac0a338f.png?resizew=158)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87136d5f4908fa04dd99bc35a16f393.png)
您最近一年使用:0次
7 . 如图所示,在四棱锥
中,
底面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/3213df0b-c6b4-4afd-9f3f-99f55f4fcc80.png?resizew=151)
(1)求证:
;
(2)若
,求平面
和平面
所成的角的正弦值.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d40978fbe52316daaaa6bdbb403fea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/3213df0b-c6b4-4afd-9f3f-99f55f4fcc80.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2751630b7353ff6bce1e8e06a2a424e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
解题方法
8 . 将四棱锥
沿棱展开为平面图形,如图所示.若
,
,
,
,
,
,则在展开图中,
两点之间的距离![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9214112843303e45a4d9dc20507ed1.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e07a099bf87e471b94bc97f0249daf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074a5b4d376ae0d7648d97b79be0b65d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d829c51c819076d094facd9dffe2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b7efcc776e3479d01484cd468c6894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa5088fedf996af3d7c50a39bdaae73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be94b5ac27724cd0e43541759203784e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0698ef3a8f862a82245d97691eba628f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9214112843303e45a4d9dc20507ed1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c6cb2c6f-7ab3-445d-8449-1c3850cd7f7f.png?resizew=171)
您最近一年使用:0次
9 . 如图,在三棱柱
中,底面是边长为
的正三角形,已知平面
平面
,点
为棱
的中点,且
.
(1)求证:
;
(2)若直线
与底面
所成的角为
,求二面角
余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0c892fa3699be6f3b91013c644e773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/5ea077cdc5c3aee9e46bf679477cb201.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/2ecca039-154d-41cd-9e83-341b19058e7c.png?resizew=185)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae2bad8d047004cbd8d4812710ba887.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddd2c1429318aba357972d600cf2cd3.png)
您最近一年使用:0次
解题方法
10 . 如图,在三棱柱
中,底面是边长为
的正三角形,已知平面
平面
,点
分别为棱
,
的中点,且
.
(1)求证:
平面
;
(2)若直线
与底面
所成角为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0c892fa3699be6f3b91013c644e773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea077cdc5c3aee9e46bf679477cb201.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/9d1b89a4-9d2d-408f-93d3-9000d66fb48a.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42605242ae45b6223b23b7a70a2b1618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61dc0fec2de4694075281e882d3c5ac.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6e972f1c678da0a16e8b532321ce4.png)
您最近一年使用:0次