名校
解题方法
1 . 如图,四棱锥
中,平面
底面ABCD,
是等边三角形,底面ABCD为梯形,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/3ef54571-0ce4-45a2-a19e-d531d46feedc.png?resizew=177)
(1)证明:
;
(2)求A到平面PBD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ad6a0124359e8b9f7649cf0bff51ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36aae82d53f2a35d2f95f467bd5b76cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3f8ecc57e62a8ef9b5be34ea6c963c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/3ef54571-0ce4-45a2-a19e-d531d46feedc.png?resizew=177)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)求A到平面PBD的距离.
您最近一年使用:0次
2021-02-28更新
|
364次组卷
|
14卷引用:福建省漳州市2019届高三毕业班高考模拟(一)试卷数学(文)试题
福建省漳州市2019届高三毕业班高考模拟(一)试卷数学(文)试题【全国校级联考】重庆市中山外国语学校2019届高三上学期开学考试(9月)数学(文)试题东北师范大学附属中学2018届高三第五次模拟考试数学(文科)试题【全国百强校】辽宁省大连八中2019届高三(上)期中数学试题(文科)四川省宜宾市叙州区第二中学校2019-2020学年高三下学期第二次月考数学(文)试题四川省成都七中2020-2021学年高三入学考试数学文科试题四川省成都市第七中学2020-2021学年高三上学期开学考试数学(文)试题四川省简阳市阳安中学2020-2021学年高三10月月考数学(文)试题新疆实验中学2021届高三10月月考数学试题河北省邯郸市大名县一中2020-2021学年高二(实验班)上学期10月半月考数学试题安徽省滁州市定远县育才学校2021届高三下学期开学考试数学(文)试题江西省南昌市第十中学2022届高三下学期第一次月考数学(文)试题辽宁省阜新市第二高级中学2022-2023学年高二上学期期中数学试题贵州省黔西南州金成实验学校2023-2024学年高二上学期第一次月考数学试题
名校
解题方法
2 . 如图,在直三棱柱
中,
,
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/394bb9a0-8ba4-4658-b11d-07e6a2177303.png?resizew=162)
(1)求证:
平面
;
(2)若异面直线
和
所成角的余弦值为
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/394bb9a0-8ba4-4658-b11d-07e6a2177303.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c920d02068d0e63ffdab70786c526d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8f19687a166c3022c81a831127dabd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb420e9a5faa91baf74a2f687b30f514.png)
您最近一年使用:0次
2019-01-31更新
|
6124次组卷
|
5卷引用:【市级联考】福建省漳州市2019届高三第一次教学质量检查测试文科数学试题
3 . 如图,在四面体
中,截面
是平行四边形.
![](https://img.xkw.com/dksih/QBM/2018/10/15/2054218165444608/2056842180435968/STEM/1a16c2eff56746378a89b778daa528a1.png?resizew=174)
(1)求证:
截面
;
(2)若截面
是正方形,求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://img.xkw.com/dksih/QBM/2018/10/15/2054218165444608/2056842180435968/STEM/1a16c2eff56746378a89b778daa528a1.png?resizew=174)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(2)若截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
2018-08-31更新
|
1159次组卷
|
6卷引用:福建省龙海市第二中学2017-2018学年高一下学期第二次(6月)月考数学试题
名校
解题方法
4 . 在棱长为
的正方体
中,
分别是
的中点,过
三点的平面与正方体的下底面相交于直线
;
(1)画出直线
;
(2)设
,求
的长;
(3)求
到
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2403734bfa7f845afaf883213548656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bbe13f5c674ba211bc31948cc91151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/773bd718-81f0-4a60-9036-136944228309.png?resizew=169)
(1)画出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3205333c4db3a336a8351de593266351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
5 . 已知E、F、G、H为空间四边形ABCD的边AB、BC、CD、DA上的点,且EH∥FG.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572939676041216/1572939682160640/STEM/d20c37d99e77447189445021978d5a55.png)
求证:(1)EH∥面BCD
(2)EH∥BD.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572939676041216/1572939682160640/STEM/d20c37d99e77447189445021978d5a55.png)
求证:(1)EH∥面BCD
(2)EH∥BD.
您最近一年使用:0次
6 . 如图,在直三棱柱
中,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572939676041216/1572939682217984/STEM/7a3c78ac67824772be740f10e0d3d50a.png)
求证:(1)
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4557a368725226f2c8ea2efb7d30e478.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e198f91d52d3dfa1533df97fbedcd8f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572939676041216/1572939682217984/STEM/7a3c78ac67824772be740f10e0d3d50a.png)
求证:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4557a368725226f2c8ea2efb7d30e478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4557a368725226f2c8ea2efb7d30e478.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d2c2d5a53396dcf826b375440cc3a.png)
您最近一年使用:0次
7 . 如图,在底面是矩形的四棱锥
中,
⊥平面
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/d50468245fc6415d8c617a08ee71c68d.png)
(1)求证:平面
⊥平面
;
(2)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/e4129349c3574b7ea72971fcdfd79a53.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/98577b7fafad4178a214b96c08b8d43d.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/2687cff4817a4b3eb175e156f52dcb77.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/eff69aea52fc4cb69a349ad08ce48ed7.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/2f81576d50d148a9a3a52050c8d20e31.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/52627e3c96cb4d9a941db57c0d1b3c49.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/99281286eb3a488cab6292f20eeccf45.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/d50468245fc6415d8c617a08ee71c68d.png)
(1)求证:平面
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/55242a6aa269430dacdf5f86d4a8afa1.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/3ebc4e5b4401493ba34224990c6c386e.png)
(2)求二面角
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572631672225792/1572631678066688/STEM/6d47ef5e472048ceac39f48de13f791a.png)
您最近一年使用:0次
8 . 如图,在底面是矩形的四棱锥P﹣ABCD中,PA⊥平面ABCD,PA=AB=2,BC=2,E是PD的中点.
![](https://img.xkw.com/dksih/QBM/2016/3/28/1572560317906944/1572560324009984/STEM/78be1c9a15914e3688580a427dc9d442.png)
(1)求证:平面PDC⊥平面PAD;
(2)求二面角E﹣AC﹣D所成平面角的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/3/28/1572560317906944/1572560324009984/STEM/78be1c9a15914e3688580a427dc9d442.png)
(1)求证:平面PDC⊥平面PAD;
(2)求二面角E﹣AC﹣D所成平面角的余弦值.
您最近一年使用:0次
9 . 如图,在直三棱柱
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/3/28/1572559566585856/1572559572484096/STEM/c1598c1916cc46e293f829ea35779147.png)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df209c58c4cc146ef62100e6d3b068d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e199a5d02bfb5b869221e61d31969bea.png)
![](https://img.xkw.com/dksih/QBM/2016/3/28/1572559566585856/1572559572484096/STEM/c1598c1916cc46e293f829ea35779147.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3da59ed9a8bc1877e5c7d00560fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a486d75becfb835e4f6ef6b40333968.png)
您最近一年使用:0次
10 . 如图,已知四棱锥
的底面为菱形,
,
,
.
(Ⅰ)求证:
;
(Ⅱ)在线段
上是否存在点
,使得直线
和平面
所成角
的正弦值为
?若存在,请说明点
位置;若不存在,请说明不存在的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e0ba32fcadd4114a3c52b52c3aea23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d539a68184fbd0ef4aa27d5bff31136.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(Ⅱ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a7dd471434c923f76809dfa5ee183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2016-12-03更新
|
892次组卷
|
3卷引用:2016-2017学年福建省漳州市第一中学高二上学期期末考试数学(理)试卷