10-11高二下·辽宁抚顺·期末
名校
解题方法
1 . 如图,已知PA⊥矩形ABCD所在平面,M、N分别为AB、PC的中点;
![](https://img.xkw.com/dksih/QBM/2021/10/18/2832078255874048/2834117571584000/STEM/28c99d28-f404-416e-ae0a-5abc18dee71b.png?resizew=287)
(1)求证:MN//平面PAD;
(2)若
,求证:MN⊥平面PCD.
![](https://img.xkw.com/dksih/QBM/2021/10/18/2832078255874048/2834117571584000/STEM/28c99d28-f404-416e-ae0a-5abc18dee71b.png?resizew=287)
(1)求证:MN//平面PAD;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb6823ce3888cb560cfa4984dc2f307.png)
您最近一年使用:0次
2021-10-21更新
|
450次组卷
|
7卷引用:重庆市第十八中学2021-2022学年高二上学期10月考试数学试题
重庆市第十八中学2021-2022学年高二上学期10月考试数学试题(已下线)2010-2011学年辽宁省抚顺市六校联合体高二下学期期末考试数学甘肃省平凉市庄浪县第一中学2019-2020学年高一第二学期期中考试数学试题福建省泉州市四校(晋江磁灶中学等)2019-2020学年高一下学期期中联考数学试题(已下线)河北省中等职业学校对口升学考试全真模拟冲刺卷数学试题十五(已下线)4.3.2 空间中直线与平面的位置关系广西桂林市奎光学校2021-2022学年高一下学期热身考试数学试题
名校
2 . 已知三棱柱
,
,侧面
为矩形,面
面
.
![](https://img.xkw.com/dksih/QBM/2021/7/10/2761063105978368/2762750065115136/STEM/a3565cec-9e6d-45cc-a498-0e24e980763a.png?resizew=281)
(1)求证:
;
(2)若二面角
的余弦值为
,
为
中点,求
与面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ddc3178cc8ac2e034fe3b1723b4bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
![](https://img.xkw.com/dksih/QBM/2021/7/10/2761063105978368/2762750065115136/STEM/a3565cec-9e6d-45cc-a498-0e24e980763a.png?resizew=281)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b872d508016940c461cd7880c88b7f.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c86be02bec7e9604c93233fd482de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8550fbd7938e0d8639462ac52a6dad1f.png)
您最近一年使用:0次
2021-07-12更新
|
791次组卷
|
3卷引用:重庆市南开中学校2020-2021学年高一下学期期末数学试题
重庆市南开中学校2020-2021学年高一下学期期末数学试题(已下线)一轮复习大题专练51—立体几何(线面角3)—2022届高三数学一轮复习湖北省襄阳市第三中学2022-2023学年高二上学期12月月考数学试题
名校
3 . 如图,在三棱柱ABC-A1B1C1中,已知AB⊥侧面BB1C1C,AB=BC=1,BB1=2,∠BCC1=
.
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779524736557056/2782329421832192/STEM/a0ec80d1-3f1e-4cb3-b8c6-069d02820fd3.png?resizew=259)
(1)求证:C1B⊥平面ABC;
(2)设
,且平面AB1E与BB1E所成的锐二面角的大小为30°,试求λ的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779524736557056/2782329421832192/STEM/a0ec80d1-3f1e-4cb3-b8c6-069d02820fd3.png?resizew=259)
(1)求证:C1B⊥平面ABC;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96241188e314807d197f59dd63cb8b7.png)
您最近一年使用:0次
2021-08-09更新
|
442次组卷
|
2卷引用:重庆市育才中学2022届高三上学期高考适应性考试一数学试题
名校
4 . 如图1所示,在等腰梯形ABCD中,
,
,
,
,把
沿BE折起,使得
,得到四棱锥
.如图2所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/7397b7d8-85fc-4ffc-801f-87e256e9fefd.png?resizew=378)
(1)求证:
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c897a54f2e36bc4b52fba74b41c89d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75929268210da5976bc37d080da030dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/7397b7d8-85fc-4ffc-801f-87e256e9fefd.png?resizew=378)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
您最近一年使用:0次
2021-07-13更新
|
841次组卷
|
2卷引用:重庆市巴蜀中学2020-2021学年高二下学期期中考试数学试题
14-15高三上·广东广州·阶段练习
解题方法
5 . 如图(1),在直角梯形
中,
,
,
,
,将
沿
折起,使平面
平面
,得到几何体
,如图(2)所示.
![](https://img.xkw.com/dksih/QBM/2020/12/2/2605704653438976/2618268718120960/STEM/8442929e94784c26bba670437547a002.png?resizew=279)
(1)求证:
平面
;
(2)求几何体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32e1b499d6b25ee132abcdd3f3cd288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://img.xkw.com/dksih/QBM/2020/12/2/2605704653438976/2618268718120960/STEM/8442929e94784c26bba670437547a002.png?resizew=279)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)求几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
您最近一年使用:0次
2020-12-20更新
|
270次组卷
|
9卷引用:重庆市万州纯阳中学2020-2021学年高二上学期第一次月考数学试题
重庆市万州纯阳中学2020-2021学年高二上学期第一次月考数学试题(已下线)2015届广东省广州市第六中学高三上学期第一次质量检测文科数学试卷2014-2015学年河北省满城中学高一下学期期中文科数学试卷2015-2016学年山西省长治一中高二(下)期中数学试卷(文科)北京市第二中学2016-2017学年高一下学期期末模拟数学试题(已下线)【新东方】杭州高二数学试卷250山西省怀仁市重点中学2019-2020学年高二上学期期末数学(文)试题(已下线)综合练习模拟卷02-2021年高考一轮数学(文)单元复习一遍过广西桂林市2021-2022学年高二下学期期末质量检测数学(理)试题
名校
解题方法
6 . 如图,在以
、
、
、
、
为顶点的五面体中,
平面
,
,
,
.
的面积
且
为锐角.
![](https://img.xkw.com/dksih/QBM/2020/9/19/2553315770621952/2553361467432960/STEM/b07598a76cde41108c6680361b1e96f4.png?resizew=200)
(1)求证:
平面
;
(2)求三棱锥
的体积
.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdd872d41982e7b50ed2aba66595f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922f76192990e3a69805209d58586987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c343fddb5d98905bb22b9b08b15f3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://img.xkw.com/dksih/QBM/2020/9/19/2553315770621952/2553361467432960/STEM/b07598a76cde41108c6680361b1e96f4.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b0d5c6592b0c8a821c00f15f1ff1cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
2020-09-19更新
|
825次组卷
|
5卷引用:2020届重庆市第一中学高三下学期6月模拟数学(文)试题
名校
解题方法
7 . 正方体ABCD-A1B1C1D1中.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/07140f46-8ba1-425d-963b-3597bb7a9875.png?resizew=188)
(1)A1C1//平面ACB1;
(2)BD1⊥平面AB1C
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/07140f46-8ba1-425d-963b-3597bb7a9875.png?resizew=188)
(1)A1C1//平面ACB1;
(2)BD1⊥平面AB1C
您最近一年使用:0次
2020-05-24更新
|
261次组卷
|
3卷引用:重庆市朝阳中学2020-2021学年高二上学期期中数学试题
重庆市朝阳中学2020-2021学年高二上学期期中数学试题广西靖西市第二中学2019-2020学年高一下学期开学考试数学试题(已下线)专题03直线与平面的位置关系(4个知识点6种题型)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)
名校
解题方法
8 . 如图,长方体
中,
,
,
是棱
上的点,且
.
![](https://img.xkw.com/dksih/QBM/2020/5/10/2459914290159616/2462533617451008/STEM/a6df6e9912b044da859bc41ee3417690.png?resizew=174)
(1)求长方体被平面
分得的两部分体积之比(大比小);
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc416a5b8dc234628e7475387888d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92d8e0c3c68eecfdfad9fa8381adc4e.png)
![](https://img.xkw.com/dksih/QBM/2020/5/10/2459914290159616/2462533617451008/STEM/a6df6e9912b044da859bc41ee3417690.png?resizew=174)
(1)求长方体被平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,四棱锥
的底面是边长为1的正方形,
底面
:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/ca04ab8c-5440-4982-a49b-1e5effec526d.png?resizew=163)
(1)求证:
;
(2)设棱
中点为
,求异面直线
与
所成角大小;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c56bc25c0f39f2099eec0f92636859.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/ca04ab8c-5440-4982-a49b-1e5effec526d.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5570c53f7794d3dd2ba733e303249f8d.png)
(2)设棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2020-02-10更新
|
171次组卷
|
2卷引用:重庆市第七中学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,四棱锥
中,
底面
,底面
为梯形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/98c6742c-7b0b-4c1f-aa0c-4599574b3507.png?resizew=175)
(1)求证:
面
;
(2)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/307ab27e2ea44f73f834a48c07bfc59d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfc9df9c661bd93b3f4f51f91534c4a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/98c6742c-7b0b-4c1f-aa0c-4599574b3507.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次