名校
解题方法
1 . 如图,已知
是平行四边形
所在平面外一点,
、
分别是
、
的三等分点(
靠近
,
靠近
);
平面
.
(2)在
上确定一点
,使平面
平面
,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28a07491270be75a3697538bec706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2 . 如图,四边形
是菱形,
平面
,
,
.
平面
;
(2)求证:平面
平面
;
(3)设点
是线段
上一个动点,试确定点
的位置,使得
平面
,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15cd53fe7b73365723ce4789bb259d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5624c7941eb3cca11d8efbe76d9af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2275e3382c378ecfd1c2560eb69c4027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
名校
解题方法
3 . 知正方体
中,
、
分别为对角线
、
上的点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c525e70f9f3d864840080804ae96819d.png)
平面
;
(2)若
是
上的点,
的值为多少时,能使平面
平面
?请给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c525e70f9f3d864840080804ae96819d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4da530384dd04ac90a025385e8b3c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943d6e170279d007a4c943f684b1c3c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8fd9020ac4827433593c1e3d503a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4da530384dd04ac90a025385e8b3c2f.png)
您最近一年使用:0次
名校
解题方法
4 . 如图是一个棱长为2的正方体的展开图,其中
分别是棱
的中点.请以
三点所在面为底面将展开图还原为正方体.
在平面
内;
(2)用平面
截正方体,将正方体分成两个几何体,两个几何体的体积分别为
,试判断体积较小的几何体的形状(不需要证明),并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec173f2991ee0a885131a8545cd0fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc6e4b7e3417414b323f89e97fa9c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c07b129ca17834b132540a253273006.png)
(2)用平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c07b129ca17834b132540a253273006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76a8c0b40531e187a2774a01588a0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30468054fb148d2f937a54fcc1d60f92.png)
您最近一年使用:0次
2024-04-26更新
|
233次组卷
|
2卷引用:云南省昆明市云南师范大学附属中学2023-2024学年高一下学期教学测评期中卷数学试卷
名校
解题方法
5 . 如图,直四棱柱
中,底面
是边长为1的正方形,点
在棱
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/0daaa5d5-1d2e-483c-b1b8-d28103505dee.png?resizew=142)
(1)求证:
;
(2)从条件①、条件②、条件③这三个条件中选择两个作为已知,使得
平面
,并给出证明.
条件①:
为
的中点;
条件②:
平面
;
条件③:
.
(3)若
为
的中点,且点
到平面
的距离为1,求
的长度.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/0daaa5d5-1d2e-483c-b1b8-d28103505dee.png?resizew=142)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0af20277067fdd1bf5b03cea567c0a84.png)
(2)从条件①、条件②、条件③这三个条件中选择两个作为已知,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b90810b206fa24f92d84504169e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81bf7a859123936a07193592e089340a.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7542b49ab149f2be8ba6b48392bef1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81bf7a859123936a07193592e089340a.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a948b9a017c589727827d944ef1224c.png)
(3)若
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81bf7a859123936a07193592e089340a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
您最近一年使用:0次
2023-11-14更新
|
247次组卷
|
2卷引用:北京市西城区北京师范大学附属实验中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
6 . 已知圆
过点
,
,且圆心
在直线
上.
是圆
外的点,过点
的直线
交圆
于
,
两点.
(1)求圆
的方程;
(2)若点
的坐标为
,求证:无论
的位置如何变化
恒为定值;
(3)对于(2)中的定值,使
恒为该定值的点
是否唯一?若唯一,请给予证明;若不唯一,写出满足条件的点
的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02af485e17e7628fd5a3ace6e0a32ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec40ff4479edca2ed18b6cadb8db72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
(3)对于(2)中的定值,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2023-10-01更新
|
601次组卷
|
7卷引用:福建省普通高中2021-2022学年高二1月学业水平合格性考试数学试题
福建省普通高中2021-2022学年高二1月学业水平合格性考试数学试题黑龙江省哈尔滨市第九中学校2022-2023学年高二10月月考数学试题福建省南安市柳城中学2022-2023学年高二上学期11月期中考试数学试题四川省通江中学2022-2023学年高二上学期期中文科数学试题专题08B圆的方程与圆锥曲线(已下线)重难点突破16 圆锥曲线中的定点、定值问题 (十大题型)-1(已下线)专题02 期中真题精选(压轴93题10类考点专练)(2)
名校
解题方法
7 . 如图所示,底面为正方形的四棱锥
中,
,
,
,
与
相交于点O,E为
中点.
平面
;
(2)
上是否存在点F,使平面
平面
.若存在,请指出并给予证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4ad370fe836accc1b2de6807d8ae62.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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe2fe5985a27babe0199e1c0865f49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f92fb805ed4f3b08ced4b8a385fa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-08-12更新
|
927次组卷
|
9卷引用:陕西省铜川市宜君县高级中学2022-2023学年高一下学期期中数学试题
陕西省铜川市宜君县高级中学2022-2023学年高一下学期期中数学试题四川省达州外国语学校2023-2024学年高二上学期9月月考数学试题(已下线)第10讲 8.5.3 平面与平面平行-【帮课堂】(人教A版2019必修第二册)广东省茂名市华侨中学2022-2023学年高一下学期段考二数学试卷(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)(已下线)8.5.3 平面与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)吉林省长春市东北师范大学附属中学净月实验学校2023-2024学年高一上学期期中质量监测数学试题(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
名校
解题方法
8 . 如图,已知四棱锥
底面
是正方形,
,
、
是的
,
中点,
为线段
上一个动点,平面
交直线
于点
.
,平面
平面
,求证:
;
(2)若
,
,求证:
;
(3)直线
是否可能与平面
平行?若可能,请证明;若不可能,请说明理由.
![](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/f0d9ef979b9f27a28cbda6923e888ccc.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf23e73ae2a15c04bbed3981cb8e511.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89e9b125dbe5955ee4f8cf77c6d9c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2023-06-09更新
|
696次组卷
|
3卷引用:北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高一下学期期中考试数学试题
解题方法
9 . 如图,在正方体
,中,H是
的中点,E,F,G分别是DC,BC,HC的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/95825610-2015-4579-ae45-e724b0753250.png?resizew=222)
(1)证明;F,G,H,B四点共面;
(2)平面
平面
﹔
(3)若正方体棱长为1,过A,E,
三点作正方体的截面,画出截面与正方体的交线,并求出截面的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/95825610-2015-4579-ae45-e724b0753250.png?resizew=222)
(1)证明;F,G,H,B四点共面;
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de22059d7d80f24817235269e9bb1ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(3)若正方体棱长为1,过A,E,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
您最近一年使用:0次
名校
10 . 在四棱锥
中,底面ABCD为矩形,
为边长为2的正三角形,且平面
平面ABCD,E为线段AD的中点,PE与平面ABCD所成角为45°.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/1b035b89-13e8-4f45-ae39-e89085b968eb.png?resizew=181)
(1)证明:
;
(2)求证:平面
平面PBC.
![](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/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/1b035b89-13e8-4f45-ae39-e89085b968eb.png?resizew=181)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fadb171a32463365ef01f91629ffb2.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22583ac400216f5aa56a84284efe4b12.png)
您最近一年使用:0次
2023-04-23更新
|
1047次组卷
|
2卷引用:四川省成都市第七中学2022-2023学年高二下学期期中考试数学(文)试题