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1 . 如图,在矩形eqId5ce7a06ae7a34393b92b5277978ac014中,eqIdeac2e4d789004c7aa61f74ea26cd1bffeqId34c6b6e427744abfb88dc90b8c7c2111的中点,以eqId7111d4972b7c401c903ff4927c13b5ec为折痕将eqIde2eb9904c9354a4b97dfb4e167d44113向上折起,使eqId312ef2c826304089b9b0f1d1e88b0f50eqId0d15519f781f48b4bd89aa7b743a6f05,且平面eqId8f8ded0e23aa4a2b8099a14a286d66d4平面eqId32b0a8afc9814c2f8a154deafdcf7192
说明: figure
(Ⅰ)求证:eqId280518d40e72425d82b15cc5061800b3
(Ⅱ)求直线eqIdcf2da96900c948a1b3ce7cbfd420c080与平面eqIde2b8bb5226ff48c6a90f9521564efc46所成角的正弦值.
2 . 如图,二面角eqId287d2375f6724e0482d95524241e422f的大小是eqIdf1c3337151994ec4b99354c9d54f311c,线段eqId6b421ef0e2c544f8b30760f6d644dab1eqIde91ca3c935af4fe5a8eb74a5848050ffeqId99a3187c2b8f4bcc9703c74c3b72f1f3eqId417e80f1349244878d01fe90e0891f5f所成的角为eqId4023ceb292e24a45871ca56fa44d50e3.直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3与平面eqId4eb56f42ca674f2f9c9101b548763159所成的角的正弦值是(   )
说明: figure
A.eqIdf9972e3e56b641a8999bb552cc07b95cB.eqIdbf4d8b310ca74c22a7eb63a406f4674aC.eqIde4d58f42bad9461b93d451da718fc6f4D.eqId5f816d038c584dc7a249120298677ef3
知识点:
3 . 如图,在三棱锥eqIda05cf829680e460f9f2ab31071f44695中,eqId64b9b599fdb6481e9f8d9a94c102300beqId6aae9bfe020741bbb0eede8056d37208都是正三角形,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175eqId2efda802d5534f6d92d9f8af7aaec28b分别为棱eqId8a76bbe21fb549e3a9c2038d58c7a3d8eqId0627be51821d4be7b3e024a354815d64eqIdcf2da96900c948a1b3ce7cbfd420c080的中点,设直线eqId1a0830891ff846de8422ea80714ecab4与平面eqIdbff89749af234cdb8934366cdcc7e24e所成角为eqId6c9518e43fd5459798a30cfc10026e3c,则eqIdf060f94089194adb86b43f05438346cc的取值范围为_________
说明: figure
4 . 已知正方形eqId5ce7a06ae7a34393b92b5277978ac014与正方形eqId5e0971e755c24adba699c6b4816dacce所成二面角的平面角的大小为eqIdb050c41d1513409598c00ecfe0de8603eqId0743582db60f420c9cae978529e721bb是正方形eqId5e0971e755c24adba699c6b4816dacce所在平面内的一条动直线,则直线eqId1b51efe7c2fa42748ac5a6be262e2fa4eqId0743582db60f420c9cae978529e721bb所成角的正切值的最小值为(   )
A.eqIdea491c3408284d46a85ac4b9b8f0ce01B.eqIdbf4d8b310ca74c22a7eb63a406f4674aC.1D.eqIda2a0ce3781fa4c26b624f5966b7dee44
5 . 如图,边长为2的正方形eqId5122959e76284546b5f4610a8a02f714所在平面与平面eqIda670baf5d73f4d7689915a00c51820f2垂直,eqId8a76bbe21fb549e3a9c2038d58c7a3d8eqId5bc8e1134afb4130a2c2d1a5b3e30dd6的交点为eqId2381423d4cd146cab95f55527681a766eqId485e0ed66f8e483995b667bfb1bb3fa4,且eqIdd97c7f4988a04f639f6be97a82879c99
说明: figure
(1)求证:eqId9bc4e9bcc8ae4bf99e7461793883794c平面eqIdc97f045463594160af5f8eed0e81619b
(2)求直线AD与平面eqId9f4208fa07f24bc69ce1bf42c811eec2所成线面角.
6 . 如图,在三棱锥eqId97af93bc48424679a970c09ac8f447cd中,侧面eqId05196544fb324d98ac235aa95d6bfb2eeqId52c1ac29bf454ed0a275b259d12a3241是全等的直角三角形,eqId8a76bbe21fb549e3a9c2038d58c7a3d8是公共的斜边,且eqIdbe1938fa020248698a5ed4e809883552eqId97193705acca4de092cd44451677d67b,另一个侧面eqIda670baf5d73f4d7689915a00c51820f2是正三角形.
说明: figure 
(1)求证:eqId9950bc3373e64c058f478d5ca6526d77
(2)求二面角eqId886f19592d4e4b38b1a6762c35b5f993的余弦值.
7 . 如图1,已知三棱锥eqId12175c05cfe240a0b8270ee03df1962f,图2是其平面展开图,四边形eqId5ce7a06ae7a34393b92b5277978ac014为正方形,eqId7ad7a82e0b5e414991c43a0bbb3b1db1eqIdf69e87b1792d407aa0e99f63830b2285均为正三角形,eqIde2f8bc21e65f476d8e4dfb6bcc9ed5f0
说明: figure
(1)求二面角eqId9bb8e0aab2094691887976d52ad61341的余弦值;
(2)若点eqId2381423d4cd146cab95f55527681a766在棱eqIdb53b60c33a254a27b9bfd58e818cc7e6上,满足eqIde09e8c78c9d14f1ca0bf20af44a55854eqId70c9440824f24484921894919ed79da0,点eqId517584fed25c413ba8b7bb33ffa2d5c6在棱eqId98607c0b5c594f5f8410e5f50df09a51上,且eqIdb0263c92c7a145ee88a1a20193257aaf,求eqId2a736304f41a412f8362958fb5c7a074的取值范围.
8 . 已知正方体eqId588284d93dc5489295f8f224f8e30d13,求:
说明: figure
(1)异面直线eqIdce3304c847ca47f486f045a4fbfc0ecdeqId30ace6b4ce264294a0534221c1b01e26所成的角;
(2)求eqIdce3304c847ca47f486f045a4fbfc0ecd与平面eqId5ce7a06ae7a34393b92b5277978ac014所成的角.
9 . 在正方体eqId588284d93dc5489295f8f224f8e30d13中,与eqIdce3304c847ca47f486f045a4fbfc0ecdeqId1a06b2701ed24e619837f7dc479f5e9d角的面对角线的条数是________
10 . 某几何体的三视图如图所示,则该几何体的各条棱中,最长的棱与最短的棱所在直线所成角的正切值为(   )
说明: figure
A.eqIdcd9b24a6a6e5426ab775be20461174e3B.eqId807b61b62f09462994e31cf497210538C.eqId15d2088f003c4aad9745c07a7616191bD.eqId2644c4fd7d684e75ae5ed93cb3581244