组卷网>知识点选题>直线、平面平行与垂直的判定与性质
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1 . 如图,已知在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,底面eqId5ce7a06ae7a34393b92b5277978ac014是矩形,eqIde78cce043a6c43329b55788351ff3484平面eqId5ce7a06ae7a34393b92b5277978ac014eqId0f1f33dbfc2e4961a3ef0973f38fc86beqIdb60bb1649c8b41cb935771acc097167eeqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175分别是eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdd293923b221045898dcc5442f88aa67a的中点.
说明: figure
(Ⅰ)求证:eqIdfec789eef46d41f085a9535585488fc5平面eqId6bc768e544bb4cc683314bfcee6add55
(Ⅱ)求eqIdb53b60c33a254a27b9bfd58e818cc7e6与平面eqId5ce7a06ae7a34393b92b5277978ac014所成角的正弦值;
(Ⅲ)求二面角eqIdee697987e8dd469bac9e26109dddb1ac的正切值.
2 . 如图,在四棱锥PABCD中,底面ABCD为正方形,∠PAB=90°,PBPDPAABE为线段PB的中点,F为线段BC上的动点.
说明: figure
(1)求证:AE⊥平面PBC
(2)是否存在点F,使平面AEF与平面PCD所成的锐二面角为30°?若存在,试确定点F的位置;若不存在,请说明理由.
3 . 如图,在几何体eqId2588751f06594e188fec5312191ec3a6中,四边形eqId5ce7a06ae7a34393b92b5277978ac014是菱形,且eqId6c245634739143368cd437a12b59f3a3eqIda36d795513d54a13a53061be6e0f72d0平面eqId5ce7a06ae7a34393b92b5277978ac014eqIda22b26530ddb4837a8dadfae20c2083a,且eqId86798d97bc434fb7966624871a184f75
说明: figure
eqId37705e1ef6a84bbdbe88433e75932cdf)证明:平面eqId0ec00b054d7a4ee08ba566e63911d7a7平面eqIdd139ef539aa4494aae522c8777f54a4e
eqIdc052ddfbd4524f67a79e0e77c2e5656a)若二面角eqId3f4b9bf406b84e959359912b400f339aeqIdb7fe117dc1a94fbf93716ecbbcced6bd,求几何体eqId2588751f06594e188fec5312191ec3a6的体积.
4 . 如图,在直三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43中,eqIdab1b2b01ce8e4594b15830e6b67e1079eqId1a59f675e3ea4309bfb83ff3b4953b43eqId9da5ed85dcc642b6a2ee462907d9a821,点eqId2381423d4cd146cab95f55527681a766是棱eqIdea82c30b37894b1bb742dee61200db07的中点,则下列说法中正确的是(   )
说明: figure
A.eqIdd4e49fdecf234767af214da91f5369b9
B.平面eqId3027f6c378fc4eb4a272a1d38f64b9ee平面eqId9b26d52d6cbc46fda65515d6f10c26e1
C.异面直线eqId0627be51821d4be7b3e024a354815d64eqIddaf8c155668d4bc28935bf064d7c5f7d所与成的角为直角
D.过点eqId346946f1395a41008d3b3b56c9ae4fbd作平面eqId180eb7168a7544f7995aeb0ffdac6b2a的平行平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac,若eqIdc13953f2514e4c8f9c8aaaf5241c33ac交侧面eqId50dcbbdb425943e8b5a0e6b8b508d09f于线段eqId0743582db60f420c9cae978529e721bb,则eqIdefc5feeedd884cf386ca7ac33cf08b60
5 . 如图,在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,平面eqId3084aa1e379e4f168e9c2332df2ca9df平面eqId5ce7a06ae7a34393b92b5277978ac014eqId2e7652229898456d96a3004e602fc5c6eqIdf0ad309b98cf449cbb8337899f6fa4aaeqId588db7aaf8e34ddc82aa8ca1e4b643c7eqId9c5ce6570eae40159c784fc35b32bf56eqId790707287e604e1a97e1484c1457c054,点eqId93cbffaa5ae045d6ac45d1e979991c3a为棱eqIdb53b60c33a254a27b9bfd58e818cc7e6的中点.
说明: figure
(1)证明:eqIdd1c000f77c224125baf22c8802a6d817平面eqIde5632d7e0a9540bfa77df0f3f1091dc8
(2)求三棱锥eqIdbc4ee36eb33b44249b77b80bebf978a4的体积.
6 . 棱长为2的正方体eqId588284d93dc5489295f8f224f8e30d13中,eqIdbedf755e0fdb4d078d6859360706b163为正方体表面上一个动点,且总有eqId04b9bf478cee4a53a1bc7ee8d8e96c7c,则动点eqIdbedf755e0fdb4d078d6859360706b163的轨迹所围成的面积为(   )
A.eqIdefe7549d43a142158aee9b47aa9a1354B.eqIdf35f1e45d1d840c2ae8371573f781126C.6D.eqId7bcd573cee334383ad72cc4b179fcfb3
7 . 如图,在长方体eqId588284d93dc5489295f8f224f8e30d13中,eqId9c79ed4754c64b02a51d9e3a2203a70eeqId72fe3587d8244374a2b6a0904fb8d261eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175分别为棱eqIdea82c30b37894b1bb742dee61200db07eqId8f39d706a505485987ccbb3f6177d72d的中点,过eqId91a3a60f05ba4520a4dfd21420cf28ca的平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac与直线eqId774919bc48254b96a96b4a4504493e7f平行,则平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac截该长方体所得截面的面积为(   )
说明: figure
A.eqId8898c1dc81824f3098bbeae74e8f11fdB.eqId09e05062a16b4f488a1f9b4f661d0c75
C.eqIdefe7549d43a142158aee9b47aa9a1354D.eqIdee280457dcd34e788d33f78436295ba4
8 . 在四棱锥eqIddd5f333edd7c4a01b271754239943f8d中,侧面eqId42ab127176d64d389237593e8dd9c7bf底面eqId5ce7a06ae7a34393b92b5277978ac014,底面eqId5ce7a06ae7a34393b92b5277978ac014为矩形,eqIdead78591f6944789b224097f5e9043b2为等边三角形,eqId790707287e604e1a97e1484c1457c054eqId922285b1cf32406693c10c09849dafcf,点eqId93cbffaa5ae045d6ac45d1e979991c3aeqId8a76bbe21fb549e3a9c2038d58c7a3d8上,eqId234cb036ed814cec8b8fa1de3fa56fcb
说明: figure
(1)求证:eqIdb16183aa581b4939914cd894a1d7b214
(2)求二面角eqId18306063f55b4eb79b8f30acdb1a23a5的正切值.
9 . 在长方体eqId588284d93dc5489295f8f224f8e30d13中,底面eqId5ce7a06ae7a34393b92b5277978ac014是边长为2的正方形.
说明: figure
(1)若eqId2381423d4cd146cab95f55527681a766eqId8f39d706a505485987ccbb3f6177d72d的中点,试在eqId3549028b0a264a919e61d7f350198187上确定一点eqId517584fed25c413ba8b7bb33ffa2d5c6,使得eqId4c5be882d621489aa6ac4a2af149b28e平面eqIde2aee013bb9f4501bb7007908fceaaf0
(2)直线eqId30ace6b4ce264294a0534221c1b01e26与平面eqIdc711ac18f5d24d079dfcfbe392a1437f所成的角为eqId4023ceb292e24a45871ca56fa44d50e3,求四棱锥eqIdb88d40a904bf41e7a4553e5ec0f61d57的体积.
10 . 如图,已知平行四边形eqId5ce7a06ae7a34393b92b5277978ac014中,eqId2807fcad45ad4b3b8490dba6af5d22e6eqId7ff34b6deb764c09a59b578c206ea8cceqId2381423d4cd146cab95f55527681a766为边eqId0627be51821d4be7b3e024a354815d64的中点,将eqIde9b428a8af374c1ea1c3d923e0f79510沿直线eqId10381e9fca8b4095b66c934255c907b4翻折成eqIdf1127c924cc34f6aa1eb4366d7b98265,若eqId517584fed25c413ba8b7bb33ffa2d5c6为是eqId6e9e3153fca343779f77e9d76e94d641的中点,则在eqIde9b428a8af374c1ea1c3d923e0f79510的翻折过程中,下列命题正确的是(   )
说明: figure
A.线段eqId322e25d340bc4a49bcc4951064148f48的长为定值
B.异面直线eqId10381e9fca8b4095b66c934255c907b4eqId6e9e3153fca343779f77e9d76e94d641所成角为eqIdcbf8f098b4634cf49e9e651e10b7cf1d
C.直线eqId322e25d340bc4a49bcc4951064148f48与平面eqIddbbcdc1769324f6a9bae763d6573e39a所成角为定值
D.二面角eqId0fccdc2f486645c3b5d6524f89fb30b9可以为直二面角
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