解题方法
1 . 在三棱锥
中,平面
平面
,
,
.设D,E分别为PA,AC中点.
![](https://img.xkw.com/dksih/QBM/2019/4/18/2185129949167616/2185998087766016/STEM/16cc90411a0448a989d79340c45ca90b.png?resizew=185)
(Ⅰ)求证:
平面PBC;
(Ⅱ)求证:
平面PAB;
(Ⅲ)试问在线段AB上是否存在点F,使得过三点D,E,F的平面内的任一条直线都与平面PBC平行?若存在,指出点F的位置并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d9ef979b9f27a28cbda6923e888ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/2019/4/18/2185129949167616/2185998087766016/STEM/16cc90411a0448a989d79340c45ca90b.png?resizew=185)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
(Ⅲ)试问在线段AB上是否存在点F,使得过三点D,E,F的平面内的任一条直线都与平面PBC平行?若存在,指出点F的位置并证明;若不存在,请说明理由.
您最近一年使用:0次
2019-04-19更新
|
1901次组卷
|
8卷引用:2015-2016学年江苏省江阴市华士、成化、山观三校高二上期中数学卷
2 . 如图所示,四边形ABCD为矩形,四边形ADEF为梯形,AD∥FE,∠AFE=60°,且平面ABCD⊥平面ADEF,AF=FE=AB=
AD=2,点G为AC的中点.
![](https://img.xkw.com/dksih/QBM/2016/10/13/1573068666142720/1573068672376832/STEM/65411056a9f0470897393f08e23f925e.png)
(1)求证:EG∥平面ABF;
(2)求三棱锥B-AEG的体积;
(3)试判断平面BAE与平面DCE是否垂直?若垂直,请证明;若不垂直,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/2016/10/13/1573068666142720/1573068672376832/STEM/65411056a9f0470897393f08e23f925e.png)
(1)求证:EG∥平面ABF;
(2)求三棱锥B-AEG的体积;
(3)试判断平面BAE与平面DCE是否垂直?若垂直,请证明;若不垂直,请说明理由.
您最近一年使用:0次
解题方法
3 . 在边长为3的正三角形
中,
分别是
边上的点,满足
(如图
),将
折起到
的位置上,连接
(如图).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/3fa939ba-3490-4587-8f4a-fe566d482bf1.png?resizew=367)
(1)在线段
上是否存在点
,使得面
面
,证明你的结论;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9f8a4bc5b0fa59ebbc37e595b343bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942e6dafcfcbf0682856b9f25178694d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06ee44206d4e110610bc412f11f2ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2d555062f34d5a74f6d47da4ea8888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390f612b4fb72c68c2235a06efec140b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/3fa939ba-3490-4587-8f4a-fe566d482bf1.png?resizew=367)
(1)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5c6bb12e7f423a4cd888201641bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641d9688e81760c02d0dfc4ba015afb1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205c74634c028da7c24bca43c691cc3a.png)
您最近一年使用:0次
解题方法
4 . 如图,四棱锥P﹣ABCD的底面为正方形,且PA⊥底面ABCD中,AB=1,PA=2.
![](https://img.xkw.com/dksih/QBM/2016/4/13/1572592397033472/1572592402825216/STEM/1ae63a1c54fe465dab46b3499c96d2bb.png?resizew=235)
(1)求证:BD⊥平面PAC;
(2)求三棱锥B﹣PAC的体积;
(3)在线段PC上是否存在一点M,使PC⊥平面MBD,若存在,请证明;若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2016/4/13/1572592397033472/1572592402825216/STEM/1ae63a1c54fe465dab46b3499c96d2bb.png?resizew=235)
(1)求证:BD⊥平面PAC;
(2)求三棱锥B﹣PAC的体积;
(3)在线段PC上是否存在一点M,使PC⊥平面MBD,若存在,请证明;若不存在,说明理由.
您最近一年使用:0次
2016-12-04更新
|
905次组卷
|
2卷引用:2015-2016学年北京市大兴区高二上学期期末文科数学试卷
5 . 如图,四棱锥
中,底面
是正方形,
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
平面
;
(2)证明:平面
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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d4c42112e0a22f240ce2ae432e5b4d.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/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2016-12-04更新
|
617次组卷
|
7卷引用:2015-2016学年浙江金华等三市部分学校高二下学期期中数学试卷
6 . 如图,在底面是菱形的四棱锥P-ABCD中,∠ABC=60o,PA=AB,
.
![](https://img.xkw.com/dksih/QBM/2016/1/8/1572425680715776/1572425686802432/STEM/8635a6563a16430bbb2350d30cb72925.png)
(1)求证:证明:BD⊥平面PAC;
(2)求PC与平面PAB所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f448b5ea52ae7d0ee6c2c028b8993d.png)
![](https://img.xkw.com/dksih/QBM/2016/1/8/1572425680715776/1572425686802432/STEM/8635a6563a16430bbb2350d30cb72925.png)
(1)求证:证明:BD⊥平面PAC;
(2)求PC与平面PAB所成角的正切值.
您最近一年使用:0次
7 . 在直三棱柱ABC﹣A1B1C1中,BC=CC1,AB⊥BC.点M,N分别是CC1,B1C的中点,G是棱AB上的动点.
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130652385280/1573130658496512/STEM/24d7937d48514976873300487c0bfa9a.png)
(1)求证:B1C⊥平面BNG;
(2)若CG∥平面AB1M,试确定G点的位置,并给出证明.
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130652385280/1573130658496512/STEM/24d7937d48514976873300487c0bfa9a.png)
(1)求证:B1C⊥平面BNG;
(2)若CG∥平面AB1M,试确定G点的位置,并给出证明.
您最近一年使用:0次
8 . 正
的边长为2,
是
边上的高,
分别是
和
的中点(如图(1)).现将
沿翻折成直二面角
(如图(2)).在图(2)中:
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/38d5e306d13a477299f990dc0fee2ceb.png)
(1)求证:
平面
;
(2)在线段
上是否存在一点
,使
?证明你的结论;
(3)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/0675c286c3cb438585ac2f9b67d0f800.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/07963e3dadb447d091501a49411fcf5e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/7b499e7a04ba4d38b028550cb36e7705.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/0a245c041053483991cc472b42383a4d.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/18e4dd3ed4eb4c42aaff38c98423364a.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/dea62cbfc42c4007b7b7345555c57fb1.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/0675c286c3cb438585ac2f9b67d0f800.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/020534bd75fc4cce8b883c621cc13737.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/38d5e306d13a477299f990dc0fee2ceb.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/2fdddf16856c44ba9406a7429bce8253.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/74b51661ce834a34bdaf2cd3ae564b9a.png)
(2)在线段
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/dea62cbfc42c4007b7b7345555c57fb1.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/2f4bdc4497ad463db02811a5ab8a9006.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/9a9d1970ab34459ca176ba3f47098898.png)
(3)求二面角
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/4ce62353534943dd80241cd138613f57.png)
您最近一年使用:0次
9 . 如图,
中,
是
的中点,
,
.将
沿
折起,使
点与图中
点重合.
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572451654770688/1572451660800000/STEM/83a4399e41b14010900ab02ae52e5f4f.png)
(1)求证:
平面
;
(2)当三棱锥
的体积取最大时,求二面角
的余弦值;
(3)在(2)条件下,试问在线段
上是否存在一点
,使
与平面
所成角的正弦值为
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4830a5e6437787c7cfc05f8b5c3ad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81574a3738c0a314293ff7c74248971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588a2119bc5e8cdf4731828b195a7892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726e55b51fbba6a4d65b2ef305750bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c916ae010949c318995479d2f7398d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76edc7b330634a1a6634b4fc8a64d211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3e2d941cdf004fc58f17b5a42d14ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2252dec4cf2fd59caff617269567806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb27b718e125e1b51f376bd932a2319c.png)
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572451654770688/1572451660800000/STEM/83a4399e41b14010900ab02ae52e5f4f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c437e3c1ec278e50293b9d40a874732e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b839d27a59354449d78ecf36861f669f.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab89d115d30900cc054237346aa0213d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e9a244f8c763215d6690b09c090fb2.png)
(3)在(2)条件下,试问在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538018e5ef2ef2aed1fa229ea94e8aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab653ffa6acf8b28096ff54719579d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4709e7fb4cb71678ea2b651e764f7eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb18c77e6ea45a312bbd4f4ba1c0e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
您最近一年使用:0次
2016-12-04更新
|
330次组卷
|
2卷引用:2015-2016学年河南三门峡市陕州中学高二上第二次对抗赛理科数学卷
10 . 在直三棱柱ABC﹣A1B1C1中,BC=CC1,AB⊥BC.点M,N分别是CC1,B1C的中点,G是棱AB上的动点.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287347712/STEM/af60347b036b43508ebf6a5d8329bcd1.png)
(Ⅰ)求证:B1C⊥平面BNG;
(Ⅱ)若CG∥平面AB1M,试确定G点的位置,并给出证明.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287347712/STEM/af60347b036b43508ebf6a5d8329bcd1.png)
(Ⅰ)求证:B1C⊥平面BNG;
(Ⅱ)若CG∥平面AB1M,试确定G点的位置,并给出证明.
您最近一年使用:0次