1 . 在四面体ABCD中,过棱AB的上一点E作平行于AD,BC的平面分别交四面体的棱BD,DC,CA于点F,G,H
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0eac358e-d7aa-4e75-b4fd-cbe363f87349.png?resizew=152)
(1)求证:截面EFGH为平行四边形
(2)若P、Q在线段BD、AC上,
,且P、F不重合,证明:PQ∥截面EFGH
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0eac358e-d7aa-4e75-b4fd-cbe363f87349.png?resizew=152)
(1)求证:截面EFGH为平行四边形
(2)若P、Q在线段BD、AC上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7071b5ecb076a09f8d128c58f01220ee.png)
您最近一年使用:0次
2 . 斜棱柱
中,侧面
面
,侧面
为菱形,
,
,
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/4/e68c5ead-ee9f-458f-86b6-f8fd81ad7003.png?resizew=273)
(1)求证:平面
平面
;
(2)若三棱柱的所有棱长为
,求三棱柱
的体积;
(3)
为棱
上一点,若
,请确定点
位置,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.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/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/4/e68c5ead-ee9f-458f-86b6-f8fd81ad7003.png?resizew=273)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3599e2d14048d66477e736223dd591d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若三棱柱的所有棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026b53eedf11dfbc3092f93f4e66af5b.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed8668bd6037c9b676d005f56f4d2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
解题方法
3 . 如图,四棱柱
中,
平面
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/63f1e9d2-ecc8-4032-9dc2-b98cfbbbf3f4.png?resizew=179)
(1)证明:
;
(2)若
,
,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca48b3c0535d84f53352e4166a7c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/63f1e9d2-ecc8-4032-9dc2-b98cfbbbf3f4.png?resizew=179)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c9c7852b781b2bd57e8c95c78f100c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ab46164b23af7a4c4907f176e392ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb04f31343f684b9543cf638e0b320ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3367b6866aa3dff279531fa5d99c768a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
您最近一年使用:0次
2017-05-20更新
|
538次组卷
|
2卷引用:河南省豫北重点中学2017届高三4月联考数学(文)试题
4 . 一个长方体的平面展开图及该长方体的直观图的示意图如图所示.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
标记在长方体相应的顶点处(不需说明理由);
(2)在长方体中,判断直线
与平面
的位置关系,并证明你的结论;
(3)在长方体中,设
的中点为
,且
,
,求证:
平面
.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
(2)在长方体中,判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55a8898c347a62c7de2bdca3f3c7e33.png)
(3)在长方体中,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338c6c83ab4abc895ac36ab888a55be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53569e6ec795658b4fffcddeebe0f142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
您最近一年使用:0次
5 . 如图,在梯形
中,
∥
,
,
,平面
平面
,四边形
是矩形,
,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/c1ef9ef6d0d24be5acaf0fe6afcde188.png)
(Ⅰ)求证:
平面
;
(Ⅱ)当
为何值时,
∥平面
?证明你的结论;
(Ⅲ)求二面角
的平面角的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/68f5ef31f20a4c379bd10a3fb2b3b0c7.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/6d834b46b8ba429f9eed15cfd1eb8dbc.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/731e4b16edfe4950b4ba9640003d5d6b.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/e62eed1cbd894981acfdc2e5ceefb20c.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/499f825f40334c66981cab494efb74cd.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/d65c720a0c2b44dbb01f476c3d5de217.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/68f5ef31f20a4c379bd10a3fb2b3b0c7.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/28858d1fa3e74f6299c575df9a9b523e.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/6a772d000010479fb81c6d5f013b200d.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/1f4ed11a77fb421e989a852d3b3371ba.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/e1acdbac12c14748ac8bb416865a4eab.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/c1ef9ef6d0d24be5acaf0fe6afcde188.png)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/2641d41d490540b4bab05389115142dd.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/28858d1fa3e74f6299c575df9a9b523e.png)
(Ⅱ)当
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/68636c28fc74406ca34c7967d12a83e7.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/f1aa6ef2b9444e198a0005c40221ec0f.png)
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/7ad087e8e9894940880c88e036f41421.png)
(Ⅲ)求二面角
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573037998727168/1573038004748288/STEM/e2071501b19e4315af7a163d7a878aef.png)
您最近一年使用:0次
2016-12-04更新
|
453次组卷
|
2卷引用:2016届宁夏银川唐徕回民中学高三下三模理科数学试卷
6 . 如图,在直三棱柱
中,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572819806568448/1572819812835328/STEM/8faf1f84db274d4280e47d7c5e35dad1.png)
(1)求证:
平面
;
(2)若
,试在
上找一点
,使
平面
,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bbe13f5c674ba211bc31948cc91151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ec28d9a001761cef6bb3018aa7323c.png)
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572819806568448/1572819812835328/STEM/8faf1f84db274d4280e47d7c5e35dad1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41adffdf0ce71e5e3fa9b00b418cfa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fbae62ef53e398a0e7276c97e7b888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
您最近一年使用:0次
7 . 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学年福建省南安一中高一上学期期末考试数学试卷
8 . (本小题满分12分)
在三棱柱
中,侧棱
,点
是
的中点,
.
(1)求证:
∥平面
;
(2)
为棱
的中点,试证明:
.
在三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://img.xkw.com/dksih/QBM/2012/10/29/1571040204709888/1571040210337792/STEM/684428eb63694a73ac029932853f2e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad91719bd5fdc1b2d3d5298f2f44cc2.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2ac002c270a3c04febf64b08667705.png)
![](https://img.xkw.com/dksih/QBM/2012/10/29/1571040204709888/1571040210337792/STEM/a741cea3d4f347e79e31d0e22f4b1010.png)
您最近一年使用:0次
2016-12-02更新
|
938次组卷
|
3卷引用:2012-2013学年江西省上饶中学高二第一次月考理科数学试卷
(已下线)2012-2013学年江西省上饶中学高二第一次月考理科数学试卷2015届江苏省宿迁市重点中学高三下学期期初开学联考理科数学试卷2015届江苏省宿迁市重点中学高三下学期期初开学联考文科数学试卷
解题方法
9 . 如图,在四棱锥
中,
是正方形,
平面
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/20/329a7886-1b8c-4868-80a5-a789935fbd61.png?resizew=176)
(1)求证:平面
平面
;
(2)在线段
上确定一点
,使
平面
,并给出证明.
![](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/99926bf272cd757f0985c69b390ebcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3a25299c121dbb883fd3c7918d566d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/20/329a7886-1b8c-4868-80a5-a789935fbd61.png?resizew=176)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a281c31b6e501123442d141860908a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)在线段
![](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/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d8073385db872410ca88187bbb0d34.png)
您最近一年使用:0次
10 . 如图,已知正方形
和矩形
所在平面互相垂直,
,
,
是线段
的中点.用向量方法证明与解答:
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572430991204352/1572430997536768/STEM/d9a50fd20aa44e658af6b05c3c4041ad.png)
(1)求证:
∥平面
;
(2)试判断在线段
上是否存在一点
,使得直线
与
所成角为
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572430991204352/1572430997536768/STEM/d9a50fd20aa44e658af6b05c3c4041ad.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)试判断在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d539cc46b0195b1d9963a7305bcd94.png)
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