名校
1 . 如图,四棱锥
的底面为矩形,
底面
,
,
,点
是
的中点,过
,
,
三点的平面
与平面
的交线为
,则下列结论中正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/0c7c630a-15a7-4072-961b-56a1f68f19c9.png?resizew=140)
(1)
平面
;
(2)
平面
;
(3)直线
与
所成角的余弦值为
;
(4)平面
截四棱锥
所得的上、下两部分几何体的体积之比为
.
![](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/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99926bf272cd757f0985c69b390ebcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/0c7c630a-15a7-4072-961b-56a1f68f19c9.png?resizew=140)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a4afe69e9ee3c701f1f109c3a0a7d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ae72f5e5891249caa10c43224da89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
(4)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
A.1个 | B.2个 |
C.3个 | D.4个 |
您最近一年使用:0次
2021-10-14更新
|
2740次组卷
|
5卷引用:广西柳州市第三中学2022届高三3月模热身考数学(理)试题
广西柳州市第三中学2022届高三3月模热身考数学(理)试题贵州省贵阳市五校(贵阳民中 贵阳九中 贵州省实验中学 贵阳二中 贵阳八中)2022届高三上学期联合考试(二)数学(理)试题(已下线)考点33 直线与平面所成的角【理】-备战2022年高考数学典型试题解读与变式(已下线)专题2 点、直线、平面之间的位置关系-学会解题之高三数学321训练体系【2022版】(已下线)第五章 破解立体几何开放探究问题 专题一 立体几何存在性问题 微点3 立体几何存在性问题的解法综合训练【基础版】
解题方法
2 . 如图,在四棱锥
中,底面
为矩形,
平面
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/07855c7d-24eb-4423-8e07-beee009bd930.png?resizew=166)
(1)证明:
平面
.
(2)证明:
平面
.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f6967901d6c855864df01e7bf7a15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/07855c7d-24eb-4423-8e07-beee009bd930.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-04-05更新
|
836次组卷
|
6卷引用:广西横州市横州中学2020-2021学年高二下学期期末考试数学试题
名校
解题方法
3 . 如图,在多面体
中,△
是等边三角形,△
是等腰直角三角形,
,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc775691cd03e1abed66100c942eb3a8.png)
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
平面
,点
为
的中点,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/2564340d-22ea-4b98-9a30-645db6333e8d.png?resizew=180)
(1)求证:
∥平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4955368b48bff112474b81c00c05d047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc775691cd03e1abed66100c942eb3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9215d0542ede79ad53c88f1d0da10af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc775691cd03e1abed66100c942eb3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/2564340d-22ea-4b98-9a30-645db6333e8d.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9906ca0da086c36c05fe3e42cf373fe.png)
您最近一年使用:0次
2021-10-11更新
|
358次组卷
|
3卷引用:广西壮族自治区贵港市西江高级中学2024届高三上学期10月月考数学试题
4 . 如图,在四棱锥PABCD中,底面ABCD是菱形,侧面PCD是等边三角形且与底面ABCD垂直,PD=AB=4,E、F分别为AB、PC的点,且PF=
PC,AE=
AB.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/696c5b01-a307-494a-8ec9-4dd5ee4cfa88.png?resizew=202)
(1)证明:直线EF//平面PAD;
(2)若BAD=60,求三棱锥BEFC的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/696c5b01-a307-494a-8ec9-4dd5ee4cfa88.png?resizew=202)
(1)证明:直线EF//平面PAD;
(2)若BAD=60,求三棱锥BEFC的体积.
您最近一年使用:0次
2021-10-04更新
|
400次组卷
|
3卷引用:广西柳州铁一中学“韬智杯”2022 届高三上学期大联考数学(文)试题
解题方法
5 . 如图,四边形ABCD与BDEF均为菱形,FA=FC,且∠DAB=∠DBF=60°.
(2)若菱形BDEF边长为2,求三棱锥E-BCD的体积.
(2)若菱形BDEF边长为2,求三棱锥E-BCD的体积.
您最近一年使用:0次
2021-09-24更新
|
322次组卷
|
4卷引用:广西普通高校2022届高三9月摸底考试数学(文)试题
解题方法
6 . 如图,在五面体ABCDEF中,四边形ABCD是直角梯形,∠BAD=90°,BC
AD,AB=AF=BC=
AD=1,AF⊥平面ABCD,N,G分别为DF,CD的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/3/2691745387814912/2808754837700608/STEM/e49c8d85-4350-4014-81e3-970b07ab1ae7.png?resizew=277)
(1)求证:NC
平面FAB;
(2)求三棱锥E﹣ACG的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/2021/4/3/2691745387814912/2808754837700608/STEM/e49c8d85-4350-4014-81e3-970b07ab1ae7.png?resizew=277)
(1)求证:NC
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)求三棱锥E﹣ACG的体积.
您最近一年使用:0次
名校
解题方法
7 . 如图,在直三棱柱ABC﹣A1B1C1中,AB⊥BC,AA1=AC=2,BC=1,E,F分别是A1C1,BC的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/3/2691745387814912/2808754837872640/STEM/f8eab5d6-37b4-4543-8366-a990a3811684.png?resizew=204)
(1)求证:C1F
平面ABE;
(2)求三棱锥A﹣BCE的体积.
![](https://img.xkw.com/dksih/QBM/2021/4/3/2691745387814912/2808754837872640/STEM/f8eab5d6-37b4-4543-8366-a990a3811684.png?resizew=204)
(1)求证:C1F
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)求三棱锥A﹣BCE的体积.
您最近一年使用:0次
2021-09-15更新
|
480次组卷
|
4卷引用:广西钦州市第四中学2020-2021学年高一(体艺班)3月份考试数学试题
广西钦州市第四中学2020-2021学年高一(体艺班)3月份考试数学试题青海省海南州中学2021-2022学年高二上学期第一次月考数学(文)试题青海省海南州中学2021-2022学年高二上学期第一次月考数学(理)试题(已下线)8.5 空间直线、平面的平行(精练)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)
8 . 如图,在多面体ABCDEF中,平面ADEF⊥平面ABCD.四边形ADEF为正方形,四边形ABCD为梯形,且
,
是边长为1的等边三角形,BC=3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/fce5ce77-48dd-4312-b793-98246470c081.png?resizew=187)
(1)求证:
;
(2)线段BD上是否存在点N,使得直线
平面AFN?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/fce5ce77-48dd-4312-b793-98246470c081.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
(2)线段BD上是否存在点N,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544381069cb72bed5598ca5adc45ae26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a459b45690bb921bbae09065b3df9f1f.png)
您最近一年使用:0次
解题方法
9 . 如图,已知矩形ABCD所在平面外一点P,PA⊥平面ABCD,E、F分别是AB、PC的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/7/2694653767475200/2808144595755008/STEM/9100bfe6-92f3-4477-8abb-ed3e276f74e7.png?resizew=231)
(1)求证EF//平面PAD;
(2)连接AC,若∠PDA=45°,BC=2CD=4,求三棱锥A-PCD的体积.
![](https://img.xkw.com/dksih/QBM/2021/4/7/2694653767475200/2808144595755008/STEM/9100bfe6-92f3-4477-8abb-ed3e276f74e7.png?resizew=231)
(1)求证EF//平面PAD;
(2)连接AC,若∠PDA=45°,BC=2CD=4,求三棱锥A-PCD的体积.
您最近一年使用:0次
10 . 如图,在四棱锥P-ABCD中,底面ABCD是菱形,∠ABC=60°,PA⊥平面ABCD,点M、N分别为BC、PA中点,且PA=AB=2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/f25956f8-9458-4108-b1c2-c231babea7ed.png?resizew=177)
(1)证明:BC⊥平面AMN;
(2)求三棱锥N-AMC的体积;
(3)在线段PD上是否存在一点E,使得MN∥平面ACE;若存在,求出PE的长;若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/f25956f8-9458-4108-b1c2-c231babea7ed.png?resizew=177)
(1)证明:BC⊥平面AMN;
(2)求三棱锥N-AMC的体积;
(3)在线段PD上是否存在一点E,使得MN∥平面ACE;若存在,求出PE的长;若不存在,说明理由.
您最近一年使用:0次
2021-09-14更新
|
461次组卷
|
4卷引用:广西桂平市麻垌中学2020-2021学年高一3月份月考数学试题
广西桂平市麻垌中学2020-2021学年高一3月份月考数学试题(已下线)8.6 空间直线、平面的垂直(精练)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.6.2直线与平面垂直(第1课时)(练案)-2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)江西省瑞金市第二中学2021-2022学年高二上学期第一次月考数学试题