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四棱锥的底面是菱形,平面, 点的中点.

(Ⅰ)求证:平面;
(Ⅱ)求证:平面.
更新:2019/9/22难度系数:0.65题型:解答题组卷:549次
如图,在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,eqId6f782d71f5a7422aa78bd8204949ce26⊥底面eqId5ce7a06ae7a34393b92b5277978ac014eqId6bcdd2ee36c54403b8981b3d682dcf55eqId1acddecbe2a24d149cbad7e37b42bc75eqId0d4c2aa50039426baa2e6f7f2590a0c4eqId93cbffaa5ae045d6ac45d1e979991c3aeqIde9b50933e347462ea824ccc9bf51fc93中点.
figure
(Ⅰ)求证:eqId25ffd7608f1b4610be3439674d85713a平面eqId02dc5b9712104a18adc92a366a8c2455
(Ⅱ)若eqId7af9eac106e04263a9c6d8e4a2a5dcbb,求平面eqId0139652b722b49798a980270e5d2d420与平面eqId5ce7a06ae7a34393b92b5277978ac014所成锐二面角的大小.
更新:2019/9/22难度系数:0.65题型:解答题组卷:0次
平行四边形eqId5ce7a06ae7a34393b92b5277978ac014中,△eqId05196544fb324d98ac235aa95d6bfb2e是腰长为eqIdc052ddfbd4524f67a79e0e77c2e5656a的等腰直角三角形,eqId7f2136837f1c495892b18ea3cba26921,现将△eqId05196544fb324d98ac235aa95d6bfb2e沿eqId1b51efe7c2fa42748ac5a6be262e2fa4折起,使二面角eqIdd6b45960c6954316943730fe84c281a8大小为eqId022e530e1dd6453ab54467745e9df0a8,若eqId48bbb48da1fc4894a6c401302847b892四点在同一球面上,则该球的表面积为_____.
更新:2019/9/22难度系数:0.65题型:填空题组卷:0次
已知eqId0ce93bfa1f6a4a23b3258410dd19847a为直线,eqId6e2423cacf0a436582967cf8ac7776a5平面,则下列说法正确的是(  )
eqId088dad8a9ea44cd7aad52c93f76aaec5,则eqId1e5c1dc58760434b80a688a93ddde74e   ②eqIdd447e31088104f4ca49ab4655abd4bc8,则eqIdf480d8cc26064a1fabcd202b5b2c9f6c
eqIdaa07474739264d82b64a2a9ab57cc008,则eqId1e5c1dc58760434b80a688a93ddde74e    ④eqId888d7617918543b798184ba78e5b811d,则eqId92c7807f834648c68d013d419a097926
A.①②③B.②③④C.①③D.①④
更新:2019/9/22难度系数:0.65题型:单选题组卷:0次
已知三棱锥eqIda05cf829680e460f9f2ab31071f44695四个顶点均在半径为eqId7dcd2312d0bf4bb1befdfcc170e45791的球面上,且eqIda184e0181619465fb1c53f2b1d171587eqIdbaffac6b458f47bf9fcd80741ce2afe7,若该三棱锥体积的最大值为eqIdf1bd69290a464f71ac73b93c51985105,则这个球的表面积为(  )
A.eqIdd47c6063972d47d09c7770e225f11c4dB.eqId1428dfe2472d4d1aab803567ed9f3d4eC.eqId59446fe0d42943f8a5156f5e6c10d091D.eqId7681784440c04c469bb134c3ea9fb53a
更新:2019/9/22难度系数:0.65题型:单选题组卷:0次
如图,eqIdb0750d9a3f9d48dab27d1eb4abf52799eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdd5b10b2a13f148b78e0d5a1b820538fd分别是三棱锥eqId12175c05cfe240a0b8270ee03df1962f的棱eqIdc390e4cf2bc742088263f6b3d1902201eqId0627be51821d4be7b3e024a354815d64的中点,eqId06ccf904979e450d845a37f42c9bc97ceqIdfe18ffe719a14cd2a8848c7f519d9ecfeqId69f8a4c190074050a3b4f0c67e0a57c0,则异面直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIda4133d812272499891a1f8813d5747f8所成的角为(   )
figure
A.eqId4023ceb292e24a45871ca56fa44d50e3B.eqIdc49bd81ea8044d68aba97695ad0e1d5eC.eqIdf1c3337151994ec4b99354c9d54f311cD.eqIdd01b7918993a412cb774dea127f210b6
更新:2019/9/22难度系数:0.85题型:单选题组卷:0次
αβ是两个不同的平面,lm是两条不同的直线,且lαmβ,下列四个命题正确的是________.
①若lβ,则αβ;②若αβ,则lm;③若lβ,则αβ;④若αβ,则lm.
更新:2019/9/22难度系数:0.85题型:填空题组卷:111次
已知α,β是两个不同的平面,m,n是两条不同的直线,给出下列命题:
①若m∥α,m∥β,则α∥β 
②若m⊂α,n⊂α,m∥β,n∥β,则α∥β;
③m⊂α,n⊂β,m、n是异面直线,那么n与α相交;
④若α∩β=m,n∥m,且n⊄α,n⊄β,则n∥α且n∥β.
其中正确的命题是(  )
A.①②B.②③C.③④D.④
更新:2019/9/22难度系数:0.85题型:单选题组卷:183次
在正方体eqId588284d93dc5489295f8f224f8e30d13中,直线eqId3be2cc74b5df4257b116d1672859cb5e与平面eqId7f3b05bea9df4e50902fe80cbca666a1所成角的正弦值为(  )
A.eqId650bf73d6b904c6a9ee39b0dc18fea28B.eqId18c57999a18a435b8420e97c41639876C.eqIde0b8cd3018f64415bea8dce0a25d0538D.eqIdd63f3d22885343d0a95c9f27b038c637
更新:2019/9/22难度系数:0.65题型:单选题组卷:224次
如图,已知三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43,平面eqIdc473d0240fe8408eb36d7f9665ed3863平面eqId89fbdcb029be4482b52165366491c70f,eqId6e82d3b62ac24ed5b35425ee7b513530eqId73495b261cf1453db3210048a43fc690分别是eqIdc9dbadca0a844a80817431c7cb4eec69的中点.
figure
(1)证明:eqIdae7277f8763242068b2a3866c248b3c1
(2)求直线eqId1a0830891ff846de8422ea80714ecab4与平面eqIdfc72f55774494f35b26e9650072a9a27所成角的余弦值.
更新:2019/9/22难度系数:0.65题型:解答题组卷:1485次
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