1 . 如图,在四棱锥
中,
是正方形,
平面
,
,
,
,
分别是
,
,
的中点.
(
)求四棱锥
的体积.
(
)求证:平面
平面
.
(
)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/3b610c9b9948d88eda8de0fb8d1cf972.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ed2ad0f3b104a54bc7fdc3739c2a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
![](https://img.xkw.com/dksih/QBM/2017/12/28/1848045150830592/1849586916147200/STEM/3526aa4588314706bf1a7bf7805634b6.png?resizew=213)
您最近一年使用:0次
2017-12-30更新
|
721次组卷
|
2卷引用:广东省广州市海珠区第六中学2016-2017学年高一上学期期末考试数学试题
2 . 如图,在三棱柱
与四棱锥
的组合体中,已知
平面
,四边形
是平行四边形,
,
,
,
,设
是线段
中点.
![](https://img.xkw.com/dksih/QBM/2018/3/4/1894848225157120/1896491616477184/STEM/89b6b2beb2e74f3796a360b264232e7c.png?resizew=171)
(1)求证:
平面
;
(2)证明:平面
平面
;
(3)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf57ded8dd17c973bb6cdc0e248c036c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65aca81ef30f0e3e00a4c2b3c53d4846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89eac4972d99833acf112d298c6c508b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2018/3/4/1894848225157120/1896491616477184/STEM/89b6b2beb2e74f3796a360b264232e7c.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea573e28da56431d5ae98e4e7a03019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be36dd512d5692a93d787f6b14c80101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a02de156f12f2623da67dda5ceaeb3f.png)
(3)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65aca81ef30f0e3e00a4c2b3c53d4846.png)
您最近一年使用:0次
2018-03-06更新
|
739次组卷
|
2卷引用:安徽省六安市第一中学2017-2018学年高一下学期开学考试数学(理)试题
3 . 如图,在直三棱柱ABC-A1B1C1中,
,
.
(1)求证:
;
(2)若
为
的中点,
为线段
上的一点,令
,当实数
为何值时,
,写出证明过程;
(3)在(2)的条件下求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bd0c4ff8305b6722ee24dd24dee2ac.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474439663bae38bc770edb67707816ac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d765eccf29001c226df06cb6fec4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7e31c08fa7294d948720059e83631e.png)
(3)在(2)的条件下求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
![](https://img.xkw.com/dksih/QBM/2018/2/7/1877182505000960/1877962577141760/STEM/d9634eb42b334c70b056313c4ea574cd.png?resizew=248)
您最近一年使用:0次
4 . 如图,在梯形
中,
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/2017/10/28/1805179522236416/1805988278362112/STEM/172bcf233ce6477d8b3cd833d4a8f618.png?resizew=218)
(1)证明:
平面
;
(2)若
为
的中点,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.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/9d50a68fed1c23837d1267bdda5c1962.png)
![](https://img.xkw.com/dksih/QBM/2017/10/28/1805179522236416/1805988278362112/STEM/172bcf233ce6477d8b3cd833d4a8f618.png?resizew=218)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2017-10-29更新
|
513次组卷
|
2卷引用:山西省太原市师范学院附属中学2017-2018学年高二上学期第一次月考数学(理)试题
名校
解题方法
5 . 如图,在菱形
中,
⊥平面
,且四边形
是平行四边形.
![](https://img.xkw.com/dksih/QBM/2017/10/11/1793058665390080/1795120232783872/STEM/af55a97e45d5478abe96891c2a29a524.png?resizew=212)
(1)求证:
;
(2)当点
在
的什么位置时,使得
∥平面
,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ab4fdfc612c9fa2dd8ae24904192d8.png)
![](https://img.xkw.com/dksih/QBM/2017/10/11/1793058665390080/1795120232783872/STEM/af55a97e45d5478abe96891c2a29a524.png?resizew=212)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf21399dcf3682bf5d3f9cbd5eed86c.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711da913d92fc989e581bcfdfe092a18.png)
您最近一年使用:0次
2017-10-14更新
|
686次组卷
|
3卷引用:浙江省嘉兴市第一中学2017-2018学年高二10月月考数学试题
名校
解题方法
6 . 如图所示,
矩形
所在的平面,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/3ebc2af6-ee27-4b66-b513-c3f99a96fbd1.png?resizew=167)
(1)求证:
平面
;
(2)求证:
.
(3)当
满足什么条件时,能使
平面
成立?并证明你的结论.
![](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/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cca777c664ecc22e40dff4ccae6b248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/3ebc2af6-ee27-4b66-b513-c3f99a96fbd1.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaa5e336f830a3e5cd60ff7a756f3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab384f2520d76ed8fa01b31e09c1eea.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2017-10-31更新
|
1160次组卷
|
3卷引用:北京西城13中2016-2017学年高二上期期中数学(文)试题
名校
解题方法
7 . 如图所示,在四棱锥
中,
平面
,底面
是菱形,
,
,
.
为
与
的交点,
为棱
上一点,
(1)证明:平面
⊥平面
;
(2)若三棱锥
的体积为
,求证:
∥平面
.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a459372aa54090fcce9430a3cfa182f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b999123e51b75bfeea6bee373e1677e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/24/cde40a84-07f6-4a39-941e-abec3a77b9a3.png?resizew=170)
您最近一年使用:0次
2017-10-20更新
|
758次组卷
|
3卷引用:四川省成都市郫都区2018届高三阶段测试(期中)数学(文)试题
8 . 如图,正方体
中,
分别为
的中点.
(1)求证:平面
⊥平面
;
(2)当点
在
上运动时,是否都有
平面
,证明你的结论;
(3)若
是
的中点,试判断
与平面
是否垂直?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e06947327f4c41340b8713e8a6b4c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f488b85184d4e9d5fc9ccd0cfda8c5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e06947327f4c41340b8713e8a6b4c87.png)
![](https://img.xkw.com/dksih/QBM/2017/8/21/1756902440853504/1757537232633856/STEM/b379cb46221c45b4ba73b4d1ca7c8ab5.png?resizew=220)
您最近一年使用:0次
9 . 如图,四棱锥
的底面是正方形,侧棱
⊥底面
是
的中点.
(Ⅰ)求证:
∥
;
(Ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f449e8cd3075c1de5cae3a57293f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6d94889ef44776a1a60586922ee891.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
![](https://img.xkw.com/dksih/QBM/2017/11/15/1817625011290112/1819374978760704/STEM/dc9e51a78fac47e59bc20c1aae79dcbe.png?resizew=166)
您最近一年使用:0次
2017-11-17更新
|
936次组卷
|
5卷引用:广东省佛山市第一中学2017-2018学年高二上学期期中考试数学(文)试题
解题方法
10 . 如图,四棱锥
的底面是边长为
的正方形,侧棱
底面
,且
,
是侧棱
上的动点.
![](https://img.xkw.com/dksih/QBM/2017/10/21/1806565718491136/1807228388163584/STEM/c114c5abd9a243c2834a2cc99f0f6970.png?resizew=176)
(1)如果
是
的中点,求证
平面
.
(2)是否不论点
在侧棱
的任何位置,都有
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/2017/10/21/1806565718491136/1807228388163584/STEM/c114c5abd9a243c2834a2cc99f0f6970.png?resizew=176)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93a5ea2c4dab70518bed4b3f2989f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)是否不论点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
您最近一年使用:0次
2017-10-31更新
|
299次组卷
|
2卷引用:北京海淀中关村中学2016-2017高二上学期期中数学(理)试题