名校
1 . 如图,矩形
中,
,
为边
的中点,将
沿直线
翻折至
的位置.若
为线段
的中点,在
翻折过程中(
平面
),给出以下结论:
①三棱锥
体积最大值为
;
②直线
平面
;
③直线
与
所成角为定值;
④存在
,使
.
则其中正确结论的序号为_________ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8588e18e27bfebf7c81c7e3c7efb1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb79f948d408ab4fb6708bde172c5e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b9f96b8ecc3cb000bb2f030809f225.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c70966a318ef8ecf874257f5c5e5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
④存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2181c78134c310f746eab44b9124e63b.png)
则其中正确结论的序号为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/2/db8c3c80-3639-479e-8ae4-e7aeaef6394b.png?resizew=239)
您最近一年使用:0次
2022-07-01更新
|
1377次组卷
|
5卷引用:四川省遂宁中学校2022-2023学年高二上学期9月月考数学(理)试题
名校
2 . 在棱长为1的正方体
中,点M是
的中点,点P,Q,R在底面四边形ABCD内(包括边界),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
平面
,
,点R到平面
的距离等于它到点D的距离,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bfb537a63ec2e7f085c0bb6eb1b2b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fa37bb4761118ea5dcb23a8de9ee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
A.点P的轨迹的长度为![]() | B.点Q的轨迹的长度为![]() |
C.PQ长度的最小值为![]() | D.PR长度的最小值为![]() |
您最近一年使用:0次
2022-04-30更新
|
1915次组卷
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6卷引用:重庆市渝高中学校2024届高三第七次质量检测(月考)数学试题
名校
3 . 如图,已知正方体
的棱长为4,
,
分别是棱
和
的中点,
是侧面
内的动点,且
平面
,当
的外接圆面积最小时,三棱锥
的外接球的表面积为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a53f3642feb20eee0af47001b5ffe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6b87654a4b5604ea8ca50a52adb442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5758391203b4105876f9b3f62dd054.png)
![](https://img.xkw.com/dksih/QBM/2022/3/29/2946459840069632/2948598897213440/STEM/dc58b473-b3fb-4879-9eb9-b04cc32d5c24.png?resizew=167)
您最近一年使用:0次
2022-04-01更新
|
1386次组卷
|
5卷引用:重庆市石柱中学校2021-2022学年高二上学期第一次月考数学试题
名校
解题方法
4 . 如图,在棱长为1的正方体
中,P为棱
的中点,Q为正方形
内一动点(含边界),则下列说法中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/67e2df88-5a04-4e60-9457-1d2c032cc1f4.png?resizew=144)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/67e2df88-5a04-4e60-9457-1d2c032cc1f4.png?resizew=144)
A.若![]() ![]() |
B.存在Q点,使得![]() ![]() |
C.当且仅当Q点落在棱![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2022-03-23更新
|
4916次组卷
|
10卷引用:江苏省南京师范大学附属中学2022-2023学年高三上学期10月月考数学试题
江苏省南京师范大学附属中学2022-2023学年高三上学期10月月考数学试题山东省济宁市汶上县第一中学2022-2023学年高三上学期12月月考数学试题湖南省长郡中学2023届高三下学期月考(七)数学试题浙江省温州市苍南县金乡卫城中学2022-2023学年高二下学期3月第一次月考数学试题江苏省淮安市六校联盟2022-2023学年高二下学期5月学情调查数学试题河北省石家庄市正中实验中学2024届高三上学期月考(四)数学试题八省八校(T8联考)2022届高三下学期第二次联考数学试题福建省漳州市第三中学2022-2023学年高二下学期期中数学试题广东省广州市第六中学2023-2024学年高二上学期期中数学试题(已下线)空间向量与立体几何
名校
解题方法
5 . 如图,正方体
的棱长为1,
,
分别是棱
,
的中点,过直线
的平面分别与棱
,
交于点
,
,设
,给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/922c5d63-0eb3-4ee6-9681-2e41157d8945.png?resizew=165)
①四边形
一定为菱形;
②若四边形
的面积为
,
,则
有最大值;
③若四棱锥
的体积为
,
,则
为单调函数;
④设
与
交于点
,连接
,在线段
上取点
,在线段
上取点
,则
的最小值为
.
其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.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/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b25f3ea33cc08b1e2a0d9c3a9dccaf.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/91f2a9b923a355694ea487f6c5669a04.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/922c5d63-0eb3-4ee6-9681-2e41157d8945.png?resizew=165)
①四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
②若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56fa5f9c9f324859bde42ee3ca620db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
③若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b941daa059b04aab552429ae22a1661d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201cc22f3d6ba9fa2b9105086939692f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31dcf3dd29fb1df05825fb4db8e53aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffb952f86442845da723fd291564484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284750727aa2c32b2477d126daefb329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18799306b1ed4d93066f569a14513d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0998c9ee1ed743a010cd977ff3e5549.png)
其中所有正确结论的序号是
您最近一年使用:0次
2022-02-28更新
|
1147次组卷
|
5卷引用:河南省洛阳市洛宁县第一高级中学2022-2023学年高二上学期9月月考数学试题
河南省洛阳市洛宁县第一高级中学2022-2023学年高二上学期9月月考数学试题北京市中国人民大学附属中学2022届高三2月自主复习检测练习(开学测)数学试题(已下线)思想03 数形结合思想(练)--第三篇 思想方法篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》(已下线)第24节 直线、平面平行的判定与性质-备战2023年高考数学一轮复习考点帮(全国通用)(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点2 线段、距离、周长的范围与最值问题(二)【基础版】
名校
解题方法
6 . 在棱长为1的正方体
中,过点A的平面
分别与棱
,
,
交于点E,F,G,记四边形AEFG在平面
上的正投影的面积为
,四边形AEFG在平面
上的正投影的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/575dddca-67ce-4b6d-813f-c498aba50680.png?resizew=146)
给出下面四个结论:
①四边形AEFG是平行四边形;
②
的最大值为2;
③
的最大值为
;
④四边形AEFG可以是菱形,且菱形面积的最大值为
.
则其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/575dddca-67ce-4b6d-813f-c498aba50680.png?resizew=146)
给出下面四个结论:
①四边形AEFG是平行四边形;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21cbb1c2bcbcb8391ac5a879f2ae0.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50524aaa1503092bd18419de6d851541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
④四边形AEFG可以是菱形,且菱形面积的最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
则其中所有正确结论的序号是
您最近一年使用:0次
2022-01-16更新
|
1047次组卷
|
4卷引用:北京市昌平区第二中学2022-2023学年高二上学期10月月考数学试题
北京市昌平区第二中学2022-2023学年高二上学期10月月考数学试题北京西城区2022届高三上学期期末数学试题(已下线)第02讲 空间向量的坐标表示-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第二册)(已下线)专题02 空间向量基本定理及其坐标表示压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)
名校
解题方法
7 . 如图,四棱锥
中,
是等边三角形,底面
是直角梯形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645c2acbf5a03068cba4d6dff6563976.png)
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/11/2870313655083008/2875145049554944/STEM/7aa1701bd041479fa2643d9c8faf3b4e.png?resizew=266)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
平面
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645c2acbf5a03068cba4d6dff6563976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96fac11d72f72c805dbddb8da72d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62794ea73abc2a84aa0512c5b205eb12.png)
![](https://img.xkw.com/dksih/QBM/2021/12/11/2870313655083008/2875145049554944/STEM/7aa1701bd041479fa2643d9c8faf3b4e.png?resizew=266)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be41b05e11ba5eadaaed9a224b949774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2014·北京朝阳·二模
名校
8 . 如图,在四棱锥
中,底面
是正方形,侧面
底面
,
,
分别为
中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/d501d3cb-322e-4c1f-9add-5a4e116a7a08.png?resizew=261)
(1)求证:
平面
;
(2)求二面角
的余弦值;
(3)在棱
上是否存在一点
,使
平面
?若存在,指出点
的位置;若不存在,说明理由.
![](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/93edc7bb513f40a89173121c8570cd65.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e87d4d9a3b0f961483bf4f68be9c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931bbffda5e872703c9947eccc47ede2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/d501d3cb-322e-4c1f-9add-5a4e116a7a08.png?resizew=261)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38675b96e9409217b9e8ec34b80fff35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af558cc6819fc74127be2933360fd40.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36148e5b0d89ba45bd98b91da00bf2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14af6bf74442941c372bb708bcdcb5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2021-11-01更新
|
4050次组卷
|
12卷引用:【全国百强校】新疆乌鲁木齐市第七十中学2018-2019学年高二下学期第一次月考数学(理)试题
【全国百强校】新疆乌鲁木齐市第七十中学2018-2019学年高二下学期第一次月考数学(理)试题天津市耀华中学2020-2021学年高二(上)第一次段考数学试题辽宁省沈阳五中2020-2021学年高二10月份月考数学试题天津市静海区大邱庄中学2021-2022学年高二上学期第一次诊断性检测数学试题天津市滨海新区塘沽紫云中学2023-2024学年高二上学期第一次月考数学试题(已下线)2014届北京市朝阳二模理科数学试卷辽宁省沈阳市郊联体2019-2020学年高二上学期期末考试数学试题(已下线)2021年新高考北京数学高考真题变式题16-21题(已下线)考点35 立体几何中的综合问题-备战2022年高考数学典型试题解读与变式(已下线)专题20 立体几何综合大题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)(已下线)理科数学-2022年高考押题预测卷02(全国甲卷)(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)
名校
解题方法
9 . 如图所示,在正方体
中,过对角线
的一个平面交
于E,交
于F,给出下面几个命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/3e73408a-ef56-4ce3-992d-4ea5a27153f2.png?resizew=149)
①四边形
一定是平行四边形;
②四边形
有可能是正方形;
③平面
有可能垂直于平面
;
④设
与DC的延长线交于M,
与DA的延长线交于N,则M、N、B三点共线;
⑤四棱锥
的体积为定值.
以上命题中真命题的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/3e73408a-ef56-4ce3-992d-4ea5a27153f2.png?resizew=149)
①四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef5ea43614d815c3abb27a42dfb101b.png)
②四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef5ea43614d815c3abb27a42dfb101b.png)
③平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef5ea43614d815c3abb27a42dfb101b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1a1b7edecd3344707cf04ea3e86916.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408871c2b71ef88d6f556ce53cf73cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
⑤四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cccd2f394207778ac6542bb656790c.png)
以上命题中真命题的个数为( )
A.2 | B.3 | C.4 | D.5 |
您最近一年使用:0次
2021-10-25更新
|
2327次组卷
|
9卷引用:北京十一学校2022届高三10月月考数学试题
北京十一学校2022届高三10月月考数学试题广东省广州市真光中学2022届高三上学期11月月考数学试题甘肃省民乐县第一中学2021-2022学年上学期高三第二次诊断(12月)考试数学(理)试题(已下线)考点16 空间向量与立体几何-2022年高考数学一轮复习小题多维练(新高考版)(已下线)考点35 立体几何中的综合问题-备战2022年高考数学典型试题解读与变式(已下线)专题23 立体几何中的压轴小题-1(已下线)专题07 立体几何小题常考全归类(精讲精练)-1人教B版(2019) 必修第四册 北京名校同步练习册 第十一章 立体几何初步 11.4 空间中的垂直关系 11.4.2 平面与平面垂直(二)(已下线)第一章 点线面位置关系 专题四 共线问题 微点2 立体几何共线问题的解法综合训练【基础版】
名校
10 . 在四棱锥
中,
为等边三角形,
,
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/4c468772-4545-427d-80f7-0acc2356e067.png?resizew=198)
(1)求证:
平面
;
(2)已知平面
平面
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32450995497b9e341be832e9efad3114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4ad161a2674d823247f0d8236cae1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/4c468772-4545-427d-80f7-0acc2356e067.png?resizew=198)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5a2f5f4970ab8a1303523e23c8b24a.png)
您最近一年使用:0次
2021-10-09更新
|
1522次组卷
|
5卷引用:江西省景德镇一中2022届高三10月月考数学(理)试题