1 . 如图,已知
是圆
的直径,
,
是⊙
上一点,且
,
,
,![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/58b7a1ffe4e5482b930a0a6d7fdebad2.png)
是
的中点,
是
的中点
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/705cc4db11704f80899766db91d70849.png)
(1)求证:
平面
;
(2)求证:
平面
;
(3)求
与平面
所成角的大小
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/a8f7033605574063b78201a5947be542.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/6b2bdc394fa4468e87ae18b0ab3ed442.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/b0b9a5f28d464a56991521833f797340.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/2ec8a42656e74ba6904cc794fab96f22.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/6b2bdc394fa4468e87ae18b0ab3ed442.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/551ea62241c24d84b6777b7168f7ac97.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/665d7681c35742939fe3013e9b2d236f.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/7996597559b2473089a30e1a4bf892ef.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/58b7a1ffe4e5482b930a0a6d7fdebad2.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/bead1b0426fe433ca35c6bce48988a56.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/c8ff1ddf63dd4cfb9575583ed3107847.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/6f3df7a20a9d4551baf950d185dd2d9a.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/0fa5d8b4f19e4bf3b5b7e4181bbf289e.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/705cc4db11704f80899766db91d70849.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/3ec6a6977a1149dfa06d11584671dfcd.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/ba13ca1cff5b458fbb3f1a32761f74cb.png)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/3760772802d543f887e918d30bb3784a.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/389f4766a4834f2cbe0a3ca19c31b3f6.png)
(3)求
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/c8ff1ddf63dd4cfb9575583ed3107847.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571958740541440/1571958746202112/STEM/ba13ca1cff5b458fbb3f1a32761f74cb.png)
您最近一年使用:0次
2 . 如图,四棱锥
,侧面
是边长为
的正三角形,且与底面垂直,底面
是
的菱形,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572961266122752/1572961272643584/STEM/6aebd8b00d164319bf6a1535a43408cc.png)
(Ⅰ)求证:
;
(Ⅱ)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fbe4053a65b67949981f24c0d30b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf5cb457a768676c10da10ccfdbb2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b0c4c783dd55685bd3e88bb31c6696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba122ff4fb6c7f5a107b3ec970ad43b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9c827e46d1a395fafbf15cdd6c6c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f34602291e9e293ff64a1606e29dc.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572961266122752/1572961272643584/STEM/6aebd8b00d164319bf6a1535a43408cc.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac0e1293aae6c92e1d5d255cb16077f.png)
(Ⅱ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0b669ef4514f24ee09adeff7f41238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9127c2f1a2ad85020d558953f2c2199a.png)
您最近一年使用:0次
3 . 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)
您最近一年使用:0次
4 . 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)
您最近一年使用:0次
5 . 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)
您最近一年使用:0次
6 . 如图,三角形△PDC所在的平面与长方形ABCD所在的平面垂直,PD=PC=4,AB=6,BC=3,点E是CD的中点,点F、G分别在线段AB、BC上,且AF=2FB,CG=2GB.
(1)证明:PE⊥FG;
(2)求二面角P﹣AD﹣C的正切值;
(3)求直线PA与直线FG所成角的余弦值.
您最近一年使用:0次
2016-12-03更新
|
4745次组卷
|
4卷引用:2015年全国普通高等学校招生统一考试理科数学(广东卷)
2015年全国普通高等学校招生统一考试理科数学(广东卷)(已下线)专题23 立体几何解答题(理科)-1专题30立体几何与空间向量解答题(第一部分)四川省宜宾县第二中学校2017-2018学年高一下学期期末模拟数学试题
7 . 如图,四棱锥
中,底面
为平行四边形,
底面
,
是棱
的中点,
且
.
![](https://img.xkw.com/dksih/QBM/2017/9/2/1765395891019776/1766284314329088/STEM/8d6d454cd5a04b7cb0322403aa363d9e.png?resizew=220)
(1)求证:
平面
;
(2)如果
是棱
上一点,且直线
与平面
所成角的正弦值为
,求
的值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890c5b938c7a39a891faeaac4d77aee8.png)
![](https://img.xkw.com/dksih/QBM/2017/9/2/1765395891019776/1766284314329088/STEM/8d6d454cd5a04b7cb0322403aa363d9e.png?resizew=220)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)如果
![](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/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d109733379365295b93c58769d2019.png)
您最近一年使用:0次
2016-12-13更新
|
1590次组卷
|
4卷引用:【校级联考】广东省汕头市达濠华侨中学,东厦中学2019届高三上学期第三次联考数学(理)试题
8 . 已知平行四边形
,
,
,
,
为
的中点,把三角形
沿
折起至
位置,使得
,
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572037567160320/1572037572517888/STEM/cdb7ec85fe5c4e65804133d4ebbc3ceb.png)
(1)求证:
;
(2)求证:面
面
;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/d0e1d24e6954a9736aa6ed412fa43bdf.png)
![](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/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502fc5e3c7f636aac9064ec69018c95c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572037567160320/1572037572517888/STEM/cdb7ec85fe5c4e65804133d4ebbc3ceb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ab1af4b3c939b0b1f819e831e32e0.png)
(2)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83716c0f110a635037adbffc7bbbb183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483f030abf61c6a0882d656d63cf4512.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516dfcfba39af76a6fffa94ac307f581.png)
您最近一年使用:0次
9 . 如图(1),
是直径
的圆上一点,
为圆
的切线,
为切点,
为等边三角形,连接
交
于
,以
为折痕将
翻折到图(2)所示
的位置,点
为平面
外的点.
![](https://img.xkw.com/dksih/QBM/2011/5/23/1570217778290688/1570217783820288/STEM/857ee6a3118946339da7ae8739e29be4.png?resizew=330)
(1)求证:异面直线
和
互相垂直;
(2)若
为
上一点,且
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b280088a8f97b52c2145bc709434e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2011/5/23/1570217778290688/1570217783820288/STEM/857ee6a3118946339da7ae8739e29be4.png?resizew=330)
(1)求证:异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8459bfe1dd87957f217ffcd0d10f6f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e89e99ab9c1ece0cc5c3bbabaa97de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fc56bf641c7b18a562dc6c1c8290bc.png)
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10 . 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)
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