在五面体
中,
,
,
,
,
.
(1)证明:
;
(2)给出①
;②
;③平面
平面
.试从中选两个作为条件,剩下一个作为结论,可以让推理正确,请证明你的推理,并求出平面
和平面
夹角的余弦值.
注:如选择不同组合分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1773fc257a6f487d80c422887dd56d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856e8dc5903774a95bd29dcc2c9877bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35112927cf711e1c9fa4c7dd392465b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f94ab32614c7ec18fd8a7549d712d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b0bdbac7874fc0784ae7dfc33e6b6b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/75767d45-1505-4025-8347-da9cfc62ad40.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b5c1c5518b9332a2fb209c3621c700.png)
(2)给出①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e3f834d569575e10b7b7af40ff4548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff113d0df4877b8877721b05afb0321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5352d28609d1b3d09a0a29d023d1bb72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61510c34c5795d7261569b4d09098271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
注:如选择不同组合分别解答,按第一个解答计分.
更新时间:2024-02-19 17:56:22
|
相似题推荐
解答题-问答题
|
适中
(0.65)
【推荐1】在
中, 已知
.
(1)若
,求
的值;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c65edad25ddd666cdce0d7e5afefc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5170bdabc30f420e0576438ae80c3d23.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b728fce49f6933bd769c23b4d97cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6402f1010e94be78552ed4c45548b1b8.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐2】已知
的内角A,B,C所对的边分别为
.
(1)求角C;
(2)若AC边上的高长为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aedecbb2114cc0fdbfbbb8cc2236d88.png)
(1)求角C;
(2)若AC边上的高长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ab7a4d7ee6813f40f7939d7c57dfc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
您最近一年使用:0次
【推荐1】已知四棱锥
的底面
是直角梯形,
,
,
,
,E为CD的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/8b821c62-ec0c-495e-9ae1-e321f1e913e5.png?resizew=161)
(1)证明:平面
平面
;
(2)若
,PC与平面
所成的角为
,试问在侧面PCD内是否存在一点N,使得
平面PCD?若存在,求出点N到直线PD的距离;若不存在,请说明理由.
![](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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ea9d92e5c258a50af1e461c7388894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaef9e92d148afff22761d5e027d3ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/8b821c62-ec0c-495e-9ae1-e321f1e913e5.png?resizew=161)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b69099d2b74ffbb1f365e1468bd8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6da9f598fecf6fcf41cd65b45cbe08.png)
您最近一年使用:0次
【推荐2】如图所示,四棱柱
,底面ABCD是以AB,CD为底边的等腰梯形,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/acdf1e6e-5849-40df-a305-f43535bae16c.png?resizew=200)
(1)求证:平面
平面ABCD;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc28e69c1ba0aac981256887f7dfa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569903d710380fb96a97c2e140f71620.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/acdf1e6e-5849-40df-a305-f43535bae16c.png?resizew=200)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c43aa55fb8c3cee4bc7a92bb20463d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bb6c309a2063ae910551726027f881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3052b9822ad39d3b344fa315ae232e0.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐1】已知在三棱柱
中,底面
是正三角形,
底面ABC,
,
,点E,F分别为侧棱
和边
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/21/31cbf7c6-9b0f-458e-a753-0cf0c63e4e7f.png?resizew=125)
(1)求证:
平面ACE;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1192b3111a6dad01bba5227472bb4072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/21/31cbf7c6-9b0f-458e-a753-0cf0c63e4e7f.png?resizew=125)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57e0d440e8ccf29fe5f9b3605ad27ca.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐2】在四棱锥
的底面
中,
∥
,
,
平面
,
是
的中点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f7d901449341de851c7de534e5f8a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/92cfbe9e-7b85-498c-aa05-7d1e3b506eb7.png?resizew=138)
(1)求证:
∥平面
;
(2)求二面角
的余弦值;
(3)在线段
内是否存在点
,使得
?若存在指出点
的位置,若不存在,请说明理由.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/42f7d901449341de851c7de534e5f8a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/92cfbe9e-7b85-498c-aa05-7d1e3b506eb7.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f457418e6a7e21f0ed0bf490a3709c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed92f62e3c8bbe5890738f0a49e171a.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐3】
是
的直径,点
是
上的动点,过动点
的直线
垂直于
所在的平面,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/50773690-fa34-43b9-bdf0-85b9932bf7d9.png?resizew=192)
(1)试判断直线
与平面
的位置关系,并说明理由 ;
(2)若已知
,求二面角
的余弦值的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/50773690-fa34-43b9-bdf0-85b9932bf7d9.png?resizew=192)
(1)试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af57d63e83ef0e183add10cd6beec65b.png)
(2)若已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f089cf8176b8e324de8b6d1fe9b39112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab90260ccf4830de2dae09083d868f6.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
解题方法
【推荐1】如图,五面体
的底面
是矩形,
∥底面
,
到底面
的距离为1,
.
平面
;
(2)设平面
平面
.
①证明:
底面
;
②求
到底面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca9eb9126c7053574c62b897582ad49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c20bda518870f0e27a5c1636206458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6290c9cefc2a4c5fa2325f80cb4863b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48abba67b697688749cf92b8c7205161.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.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,底面ABCD为直角梯形,BC
AD,∠ADC=90°,BC=CD
AD=1,E为线段AD的中点.PE⊥底面ABCD,点F是棱长PC的中点,平面BEF与棱PD相交于点G.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/df923fa7-3a5c-4973-84fa-82df55962434.png?resizew=138)
(1)求证:BE
FG;
(2)若PC与AB所成的角为
,求直线PB与平面BEF所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50a39604477d1d9326eb455cda2e838.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/df923fa7-3a5c-4973-84fa-82df55962434.png?resizew=138)
(1)求证:BE
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)若PC与AB所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
您最近一年使用:0次