如图,在四棱锥
中,底面
是正方形,侧棱
底面
,
,
是
的中点.
(1)证明:
平面
;
(2)求
与底面
所成的角的正切值.
![](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)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466fabcaac59132fea648ff35342ec9d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2010/9/23/1569838450851840/1569838456045568/STEM/accbc2d0-6f79-424d-9cfe-57a705485c4f.png?resizew=280)
9-10高三·四川成都·阶段练习 查看更多[1]
(已下线)四川省成都市玉林中学2011届高三九月诊断性数学试卷(数学文)
更新时间:2016-11-30 08:27:25
|
相似题推荐
解答题-证明题
|
适中
(0.65)
解题方法
【推荐1】如图所示的五面体
中,平面![](https://img.xkw.com/dksih/QBM/2019/5/9/2199904660062208/2200528084885504/STEM/17be5805383d4be7923939574aec09d2.png?resizew=39)
平面
,
,
,
∥
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/2b54cbdd-ab1d-4300-b671-9e1d000f3182.png?resizew=209)
(Ⅰ)求四棱锥
的体积;
(Ⅱ)求证:
∥平面
;
(Ⅲ)设点
为线段
上的动点,求证:
与
不垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://img.xkw.com/dksih/QBM/2019/5/9/2199904660062208/2200528084885504/STEM/17be5805383d4be7923939574aec09d2.png?resizew=39)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5427b7b994b860628df3d6b7a07de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d00572a90232e08932317af2a53767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/2019/5/9/2199904660062208/2200528084885504/STEM/4f92936320b040f4abde21ea625da850.png?resizew=87)
![](https://img.xkw.com/dksih/QBM/2019/5/9/2199904660062208/2200528084885504/STEM/d9608e061c314a3f9390e88e28d14601.png?resizew=83)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/2b54cbdd-ab1d-4300-b671-9e1d000f3182.png?resizew=209)
(Ⅰ)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(Ⅲ)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2019/5/9/2199904660062208/2200528084885504/STEM/52c8bafa754944f5b2b4a191fc3be689.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2019/5/9/2199904660062208/2200528084885504/STEM/3298f1d2a4984601ad15bea0baf6a984.png?resizew=29)
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【推荐2】如图,在直三棱柱ABC-A1B1C1中,E,F分别为A1C1和BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/1ed5fdc1-25f9-4846-9d69-37340500947a.png?resizew=122)
(1)求证:EF∥平面AA1B1B;
(2)若AA1=3,AB=2
,求EF与平面ABC所成的角.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/1ed5fdc1-25f9-4846-9d69-37340500947a.png?resizew=122)
(1)求证:EF∥平面AA1B1B;
(2)若AA1=3,AB=2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f8c3ba00c59e0634ed10fa85289de.png)
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名校
解题方法
【推荐1】如图,在三棱柱
中,侧面
,
均为正方形,
,
,点D是棱的
中点.
(1)求证:
平面
;
(2)求异面直线
与
所成角的大小;
(3)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/8/4afb0b38-b4be-419d-a77f-3d4d05dd9bd0.png?resizew=202)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
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适中
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【推荐2】如图,在多面体
中,
平面
,且
是边长为2的等边三角形,
.
是线段
的中点,证明:直线
面
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c5ae16a7145a28a91d45ef950a07c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0968b39e8d3a5146759340413571d0d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69dc003d123423886dba10b28b10b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d3f5f4c4419913c1232b7aae03ade.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db1d8f228c87b65a3609f825fc441d5.png)
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【推荐3】如图,在棱柱
中,底面
为平行四边形,
,
,
,且
在底面上的投影
恰为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/11/21/2597682080964608/2600396935954432/STEM/a3c760ac0ec14fdda798452d3fc7ade5.png?resizew=159)
(1)过
作与
垂直的平面
,交棱
于点
,试确定点
的位置,并说明理由;
(2)在线段
上是否存在点
,使二面角
为
?若存在,请确定点
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5028e28469730cb6931c383623ea792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb552b9e21dbaba74d11aa747790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2020/11/21/2597682080964608/2600396935954432/STEM/a3c760ac0ec14fdda798452d3fc7ade5.png?resizew=159)
(1)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8b2c5d661a0c3eaff591b027a2eeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ebb47fec53def6d404afd988c2bb571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc3257f37be3274a38ec21b7ce9ebb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ec07ba5768463e06aec1f6869f487e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b199d124fb9a5bc8438c9884f04534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐1】如图,矩形ABCD中,
,
,M为边CD的中点,将
沿直线AM翻折成
,且
,点P为线段BE的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/28/2989030003204096/2989890806292480/STEM/039fe61fd6174451bddda312ccd21473.png?resizew=285)
(1)求证:
平面AME;
(2)求直线PC与平面ABM所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f9fba8a4098c1a0515286eb8d616dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e323c08b18488d11bd8f3cd74efa971a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75929268210da5976bc37d080da030dd.png)
![](https://img.xkw.com/dksih/QBM/2022/5/28/2989030003204096/2989890806292480/STEM/039fe61fd6174451bddda312ccd21473.png?resizew=285)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2597b5554284e275367c25529c6750f.png)
(2)求直线PC与平面ABM所成角的正弦值.
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【推荐2】已知平行六面体
中,
,
,
,侧面
是菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/868d8efd-e79e-4f9d-be4e-945315c4c923.png?resizew=212)
(1)求
与底面
所成角的正切值;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68397b031b018d84d89a0373221373d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d04812fd787f9677100063fcdbd3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbb4afeaca62289bbd780e672d29868.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/868d8efd-e79e-4f9d-be4e-945315c4c923.png?resizew=212)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7b5c8b9a5efe0dbb725026390f8bed.png)
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适中
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【推荐3】如图,在四棱锥
中,底面
为菱形,
平面ABCD,
为
的中点.
与直线
相交于点
,求证:
为
的中点;
(2)若
,
,直线
与平面
所成角的大小为
,求PD的长.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b69099d2b74ffbb1f365e1468bd8fa.png)
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