如图,在直三棱柱
中,
,
,
,点D为棱BC上一点,且
,E为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898374463053824/2899264649428992/STEM/89191f062bb34b929c70edc82dffd8d5.png?resizew=200)
(1)求证:平面
平面
;
(2)求平面
与平面ADE夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e29b56159246cc50cfa21ba71241a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a8670759c61d785b9a336885df700b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898374463053824/2899264649428992/STEM/89191f062bb34b929c70edc82dffd8d5.png?resizew=200)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
更新时间:2022-01-21 15:11:56
|
相似题推荐
解答题-证明题
|
适中
(0.65)
解题方法
【推荐1】如图,在四棱锥
中,
,
,
,平面
平面
,
.
(1)求证:平面
平面
;
(2)若
与平面
所成的角为
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4672faa9f052cfc4b2dc28d9cfd042e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8deb3ca837c7289a882b54eede8172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70dd5ebefb8658a232271a5d457042a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/9e6c9d91-d368-4c70-a06b-c5cb2f8e457e.png?resizew=190)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4d775e9fb8bca58a25e75d5b21b05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
【推荐2】在四棱锥P-ABCD中,BC∥AD,PA⊥PD,AD=2BC,AB=PB, E为PA的中点.
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572146694864896/1572146700673024/STEM/d07844ac78ab4855a7e1573abc982805.png?resizew=173)
(1)求证:BE∥平面PCD;
(2)求证:平面PAB⊥平面PCD.
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572146694864896/1572146700673024/STEM/d07844ac78ab4855a7e1573abc982805.png?resizew=173)
(1)求证:BE∥平面PCD;
(2)求证:平面PAB⊥平面PCD.
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐3】如图,直四棱柱
的底面是菱形,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/22/c7e9532d-db0a-4f2a-920d-ab2238a20478.png?resizew=184)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66717dd730006aa40e73659eb65a0f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7676b9fbff1a2f3c3087efc50fcd0e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/22/c7e9532d-db0a-4f2a-920d-ab2238a20478.png?resizew=184)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a463a03c549b0dba6d90e7f16a2af.png)
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解答题-问答题
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适中
(0.65)
解题方法
【推荐1】如图1,在平面六边形ADCFBE中,四边形ABCD是边长为的
正方形,
和
均为正三角形,分别以AC,BC,AB为折痕把
折起,使点D,F,E重合于点P,得到如图2所示的三棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/c239de90-8bcb-4f72-b861-a05119877174.png?resizew=279)
(1)证明:平面PAC⊥平面ABC;
(2)若点M是棱PA上的一点,当直线BM与平面PAC所成的角最大时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec18b555d0b8547842b65edb634a85b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4a49d7f01692ba3b1bd08dcabc7faee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/c239de90-8bcb-4f72-b861-a05119877174.png?resizew=279)
(1)证明:平面PAC⊥平面ABC;
(2)若点M是棱PA上的一点,当直线BM与平面PAC所成的角最大时,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde9209b75a84c2c9ea868634f148440.png)
您最近一年使用:0次
解答题-证明题
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适中
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解题方法
【推荐2】如图,四边形
为直角梯形,其中
,
,
,点
为
的中点,以
为折痕把
折起,使点
到达点
的位置,且使
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/525b4d5e-b948-46b4-ab81-d6a041c4ab70.png?resizew=202)
(1)求证:平面
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc01b1ea3c7efd39d1454d408040d74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0acc93490a6a784eb62201d93dd93d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0672b850a28c685d0d014c8e93ca6f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaebaf8ceed245eba896f36d8ff14b5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/525b4d5e-b948-46b4-ab81-d6a041c4ab70.png?resizew=202)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8548b4b6a78b672675479fd98a4c8432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564376a88fa74090de9f7694226a6184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
您最近一年使用:0次