1 . 如图,在直三棱柱
中,平面
侧面
,且
.
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772605952/STEM/9b83dc6e25ee48d7975690c9b755fc49.png)
(1)求证:
;
(2)若
,求锐二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d7e638ee7e910e4dd7fec67b9b75da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772605952/STEM/9b83dc6e25ee48d7975690c9b755fc49.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af254745c1c19bd20e83344bee674ce7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c127b47353581fe4626d55345a5cb4eb.png)
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2 . 如图,矩形
所在的平面与等边
所在的平面垂直,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283446231040/1572283452358656/STEM/783a21cba3034167a023ebf238eaa4d9.png)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a73d381aab499a5c0a5e81cee02efd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283446231040/1572283452358656/STEM/783a21cba3034167a023ebf238eaa4d9.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94797c3647d8d188f655772f01864ce.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114535a0f82dbb18dae843f6f191a87d.png)
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3 . 如图,在四棱锥P—ABCD中,侧面PAD⊥底面ABCD,△PAD是正三角形,四边形ABCD是矩形,且
,E为PB的中点.
![](https://img.xkw.com/dksih/QBM/2015/10/10/1572254207959040/1572254213242880/STEM/b09aa55c3a8a4d28aca34f16c45fffd9.png)
(1)求证:PD∥平面ACE;
(2)求证:AC⊥PB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1d36437d9e50f560536853ecd636d4.png)
![](https://img.xkw.com/dksih/QBM/2015/10/10/1572254207959040/1572254213242880/STEM/b09aa55c3a8a4d28aca34f16c45fffd9.png)
(1)求证:PD∥平面ACE;
(2)求证:AC⊥PB
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4 . 如图,在四棱锥
中,
平面
;四边形
是菱形,经过
作与
平行的平面交
与点
,
的两对角线交点为
.
求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6153163fecdf3f410411048428ccaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e458f4503e211b542f6f30c8a34eaca5.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc5c0771b501da459f1a12e8f1ebe72.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205463117824/1572205468975104/STEM/c22d8c8a031340b1afc37b01ee5f5c77.png)
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5 . 三棱柱
的直观图及三视图(正视图和俯视图是正方形,侧视图是等腰直角三角形)如图所示,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2015/3/24/1572021623480320/1572021629509632/STEM/eedc4df3b8e04c58b6c9b8fb8d0ae369.png)
![](https://img.xkw.com/dksih/QBM/2015/3/24/1572021623480320/1572021629509632/STEM/f3073629bc6c4d579648e2b1ea658377.png)
(1)求证:
平面
;
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2015/3/24/1572021623480320/1572021629509632/STEM/eedc4df3b8e04c58b6c9b8fb8d0ae369.png)
![](https://img.xkw.com/dksih/QBM/2015/3/24/1572021623480320/1572021629509632/STEM/f3073629bc6c4d579648e2b1ea658377.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3da59ed9a8bc1877e5c7d00560fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58cab0a5fbdc54bd8f01a1659e17987.png)
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6 . 如图,在棱长为
的正方体
中,点
是棱
的中点,点
在棱
上,且满足
.
![](https://img.xkw.com/dksih/QBM/2014/3/31/1571591338311680/1571591343652864/STEM/75d2bbccc4ae4ec18050cac1fd243dc3.png)
(1)求证:
;
(2)在棱
上确定一点
,使
、
、
、
四点共面,并求此时
的长;
(3)求平面
与平面
所成二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8456cee87c4e22351affc28f3a73a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b74e3ad474d589ef154dbcda5caaa17.png)
![](https://img.xkw.com/dksih/QBM/2014/3/31/1571591338311680/1571591343652864/STEM/75d2bbccc4ae4ec18050cac1fd243dc3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed33744c92e7600d4f2642ec0892560.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fec5bd77cfc1313bc200480cc66c766.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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7 . 如图所示,在长方体ABCD﹣A1B1C1D1中,BC=2AB=4,
,E是A1D1的中点.
![](https://img.xkw.com/dksih/QBM/2016/8/17/1572981576130560/1572981581651968/STEM/7b90cd6e-b4db-430b-9c5e-7f2b760f3d10.png)
(Ⅰ)在平面A1B1C1D1内,请作出过点E与CE垂直的直线l,并证明l⊥CE;
(Ⅱ)设(Ⅰ)中所作直线l与CE确定的平面为α,求点C1到平面α的距离.
![](https://img.xkw.com/dksih/QBM/2016/8/17/1572981576130560/1572981581651968/STEM/88393b58260c4ae9a3db11dabca11181.png)
![](https://img.xkw.com/dksih/QBM/2016/8/17/1572981576130560/1572981581651968/STEM/7b90cd6e-b4db-430b-9c5e-7f2b760f3d10.png)
(Ⅰ)在平面A1B1C1D1内,请作出过点E与CE垂直的直线l,并证明l⊥CE;
(Ⅱ)设(Ⅰ)中所作直线l与CE确定的平面为α,求点C1到平面α的距离.
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8 . 如图,长方体
中,
,
,点E是线段AB中点.
证明:
;
求二面角
的大小的余弦值;
求A点到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95db5d71f0d7cdb83e2b6bb25cea42b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fa3aea72ccc36948a4a90f7368f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62191bcb4f06ed7667c470207a91cf8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbeb4e8eeb288b3cabb5c30b6af473b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557b79c2a9bc8321629c1d1c8bcf74c2.png)
![](https://img.xkw.com/dksih/QBM/2019/1/17/2120854487957504/2123462368133120/STEM/d75b15a0cba84c2b984465ee7f16dbb7.png?resizew=199)
您最近一年使用:0次
2016-12-03更新
|
987次组卷
|
2卷引用:2014-2015学年广东省揭阳市三中高二下学期第一次段考理科数学试卷
9 . 如图,三棱柱
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572046441324544/1572046447280128/STEM/2eb4475a004e4fa189b25f4cf5a7a473.png)
(1)证明:
;
(2)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee56874296cdf9d04b9e870b14646d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3b5cd3b941724ad6fe09c881b2ac6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7eb9109cd6477627ed720c267f95e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc704b0b870ff5a83d6e0d959243a4f6.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572046441324544/1572046447280128/STEM/2eb4475a004e4fa189b25f4cf5a7a473.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cedb82ecd8a0949c7073a9e87eecf0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f889876d2abb2da0e22336b8bf7e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8893ee3e4dcea0c0f355bbd25ac4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c36118a88358990f59099074284b67.png)
您最近一年使用:0次
10-11高一下·黑龙江牡丹江·期末
名校
10 . 如图,四棱锥P-ABCD中,底面ABCD为平行四边形,∠DAB=60°,AB=2AD,PD⊥底面ABCD.
(2)若PD=AD,求二面角A-PB-C的余弦值.
(2)若PD=AD,求二面角A-PB-C的余弦值.
您最近一年使用:0次
2016-12-03更新
|
3747次组卷
|
32卷引用:2015届广东省惠州市高三第二次调研考试理科数学试卷
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