如图所示,在四棱锥
中,底面
是边长为
的正方形,
平面
二面角
的大小为
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/fbbe7b72-05a9-480e-93cf-b17cbbee91b2.png?resizew=175)
(1)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab69dcbdcd191102b0daf913c730055.png)
(2)在线段
上是否存在一点
,使得点
到平面
的距离为
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a955d5dab19e35c8e2a4437dae9e93f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe11ff2c080a2346c3a0f156ebaabd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee460fa5eec406f491e514ffd6285e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6241f9ef86cd0a902cbadaf336767dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6fec562d0b646ee75abe1cce5926d1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/fbbe7b72-05a9-480e-93cf-b17cbbee91b2.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cbe73724146a6ae435dc1fa7e88b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab69dcbdcd191102b0daf913c730055.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc704b98f4ed2c7359a7a5b6498b5290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23901e208d26f1332a51d26cedab4677.png)
2019·黑龙江大庆·二模 查看更多[8]
更新时间:2019-05-08 09:43:49
|
相似题推荐
解答题-问答题
|
较难
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名校
【推荐1】如图,在四面体
中,
平面
,
,
,
.
是
的中点,
是
的中点,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/7/6c11ea64-29e8-4d1b-b9be-11f6f99c1274.png?resizew=171)
(1)证明:
平面
;
(2)若异面直线
与
所成的角为
,二面角
的大小为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e3c9755dbd39fb01de614840d230f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/7/6c11ea64-29e8-4d1b-b9be-11f6f99c1274.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b70049601f57c8a2ece170c0a9c3c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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【推荐2】如图,在四棱锥
中,底面
为直角梯形,其中
,
,
,
平面
,且
,点
在棱
上,点
为
中点.
![](https://img.xkw.com/dksih/QBM/2022/3/4/2929001405235200/2933087011979264/STEM/04d6bb868d26424893e482cde323d447.png?resizew=226)
(1)证明:若
,直线
平面
;
(2)求二面角
的正弦值;
(3)是否存在点
,使
与平面
所成角的正弦值为
?若存在求出
值;若不存在,说明理由.
![](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/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.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/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/3/4/2929001405235200/2933087011979264/STEM/04d6bb868d26424893e482cde323d447.png?resizew=226)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85ce5e111acf7162b8e1b5a3f6b220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1000f47a7a77a81c2d0bf1b1f8599f.png)
(3)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d567bdeba9b8e17d0911f594e141eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47548785e478bc5b9591341a881e3127.png)
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解题方法
【推荐3】如图,在等腰梯形
中,
,
为
上一点,且
,平面外两点
满足
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/c88880b9-37bc-4b33-a8a8-86753115c8f2.png?resizew=172)
(1)证明:
平面
.
(2)求该几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29537d324a3849c196b1fd64f362067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e32a859e1616f7a7e4202d58d030794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6e0bfb13d3403be93723a9915c07a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b5bcc9241f391dc6fb21b3713160a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7748d2239148e44784ddacc1d8e77c4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/c88880b9-37bc-4b33-a8a8-86753115c8f2.png?resizew=172)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求该几何体的体积.
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解答题-证明题
|
较难
(0.4)
名校
【推荐1】如图,四棱锥
中,底面
为平行四边形,
底面
,且
,
.
![](https://img.xkw.com/dksih/QBM/2017/11/25/1824658750365696/1825596991848448/STEM/0d911bc44d084732b6847775dc0c987f.png?resizew=175)
(1)求证:平面
平面
;
(2)如果
是棱
上的点,
是棱
上一点,
,且三棱锥
的体积为
,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/98e624e6ee68b796f70f9d35e78a8aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://img.xkw.com/dksih/QBM/2017/11/25/1824658750365696/1825596991848448/STEM/0d911bc44d084732b6847775dc0c987f.png?resizew=175)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](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/bb4f47cccdb7195f15858fcfdf644214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2329ab55ae9452449e058c89b3fc394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced22fbe85d4a749c7b0b6bbae3ea3e7.png)
您最近一年使用:0次
解答题-作图题
|
较难
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名校
【推荐2】如图为某一几何体的展开图,其中
是边长为
的正方形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21f3055411b6927d08f328da969b017.png)
,点
及
共线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/d1687fa9-e9d9-4985-84e6-39585e4167dd.png?resizew=165)
(1)沿图中虚线将它们折叠起来,使
四点重合,请画出其直观图,试问需要几个这样的几何体才能拼成一个棱长为
的正方体
?
(2)设正方体
的棱
的中点为
,求平面
与平面
所成二面角(锐角)的余弦值.
(3)在正方体
的
边上是否存在一点
,使得
点到平面
的距离为
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21f3055411b6927d08f328da969b017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0437348e1bf7c037e7e4904609b9ba2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec835ef17014181e96cfb481dc72ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e2cbbf7a93719b3196a7d931ef638f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/d1687fa9-e9d9-4985-84e6-39585e4167dd.png?resizew=165)
(1)沿图中虚线将它们折叠起来,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4457a029cd930f0052f1c80cfe06d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
(2)设正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)在正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5105eb24aa12b2163d9c7f50ec1ef2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
【推荐1】如图,为正六棱柱
,底面边长
,高
.
![](https://img.xkw.com/dksih/QBM/2020/7/15/2506613192949760/2506658161008640/STEM/cc34eae633e34193bb67422d131458fb.png?resizew=382)
(1)若
,求异面直线
和
所成角的大小;
(2)计算四面体
的体积(用
来表示);
(3)若正六棱柱为一容器(有盖),且底面边长
和高
满足:
(
为定值),则当底面边长
和高
分别取得何值时,正六棱柱的表面积与体积之比最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858be9a2f30a22cfdebeaa5bf2e45b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56b5e308d4dcc9365ea637ea5f61ff7.png)
![](https://img.xkw.com/dksih/QBM/2020/7/15/2506613192949760/2506658161008640/STEM/cc34eae633e34193bb67422d131458fb.png?resizew=382)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa276b4e08d06f216ddd96ee3fd9d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75fee3cad5e661a4a9a87183e51a52d.png)
(2)计算四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d0113d5c77146e9ee3482b2a75749c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec707e3852297341490f121f2c4a245b.png)
(3)若正六棱柱为一容器(有盖),且底面边长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84804131e0eca8d875be97cb5292e4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
【推荐2】如图,在三棱柱
中,四边形
是菱形,
分别是
的中点,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/293a9aca-ef01-4c1e-8714-8a7d693e945b.png?resizew=179)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b212ff4649b37b655010ef687a5f4fe.png)
(2)若
,点
到平面
的距离为
.求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31843423a08f214f073e0ffd85fdafb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4525c00ed908bed8ba8d353e747a858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/293a9aca-ef01-4c1e-8714-8a7d693e945b.png?resizew=179)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b212ff4649b37b655010ef687a5f4fe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731d05ce9acc78f92d88703672f70d61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
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