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1 . 如图,在棱长均相等的正四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,eqId2efda802d5534f6d92d9f8af7aaec28b为底面正方形的中心,eqId71891062a8724584af9a2c4c77cd566e分别为侧棱eqIdf83ddc861f1c4f11b2b1c1f071767666的中点,下列结论正确的是(   )
说明: figure
A.eqIddc49cd9286d9417a8e20f8c3ee338909平面eqId62a1437f28ef46a68309cb06b8b8cdf4B.平面eqIdd580816213b04d529ef40abe79b5ecda平面eqId62a1437f28ef46a68309cb06b8b8cdf4
C.eqIded96d74ee0704e7ead209997a7affd72D.直线eqIdd293923b221045898dcc5442f88aa67a与直线eqId876037be016c4316885be871978f005b所成角的大小为eqIdcbf8f098b4634cf49e9e651e10b7cf1d
解答题 | 一般(0.65) | 2021·全国高二课时练习
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2 . 如图,在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqId2efda802d5534f6d92d9f8af7aaec28b为底面eqId5ce7a06ae7a34393b92b5277978ac014的中心,eqIdbedf755e0fdb4d078d6859360706b163eqIde4682078ddd9488281e376503edb4f95的中点.在棱eqId8f39d706a505485987ccbb3f6177d72d上是否存在一点eqId75a143b898e14ccdb032561fba9da811,使得平面eqIdf35ae9fe374c4039879b74caf6f5bfe1平面eqId94c05580372343acb27c5b0ecb094951?若存在,指出点eqId75a143b898e14ccdb032561fba9da811的位置;若不存在,请说明理由.
说明: figure
3 . 如图所示,在直四棱柱eqId588284d93dc5489295f8f224f8e30d13中,底面eqId5ce7a06ae7a34393b92b5277978ac014为等腰梯形,eqId588db7aaf8e34ddc82aa8ca1e4b643c7eqId18e3ae3e255349039d6726b8293c6cabeqId6217cb5587214912851f428ffb6b5256eqIdc0ccc58b8e954a0a83b879635b3538b8eqId93cbffaa5ae045d6ac45d1e979991c3aeqId8ff7fb67f4124e8ea505f62727ae988aeqId63db14a5b4334f3ea583c8fb12b0d175分别是棱eqId8a76bbe21fb549e3a9c2038d58c7a3d8eqIdea82c30b37894b1bb742dee61200db07eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点.
说明: figure
求证:(1)直线eqIdedaa4461bef54ac49879e2204537aa73平面eqIdba3172db6a2c46e29af11c360cbda4af
(2)平面eqId9c095c25648c443698ebef0f861795ec平面eqIdba3172db6a2c46e29af11c360cbda4af
填空题 | 较易(0.85) | 2021·全国高二课时练习
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4 . 若平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac的一个法向量为eqIde165dde376b3411583d560639917a07c,平面eqId4eb56f42ca674f2f9c9101b548763159的一个法向量为eqIde112cfd07236449698e21fb40ddb6966eqIdd80209f32d0945f7a14a286b64d35d96,则实数eqId0b4fc8a120af4fab80df6ffdcf7c46f8______
5 . 下列四个正方体图形中,eqIdeb53cb7cb0274f7d8f111c60f824c243为正方体的两个顶点,eqId37933d86b6b745239039e046227114bd分别为其所在棱的中点,能得出eqIdb3d91a8ed8ec4562ade2e00e5b8e1c74平面eqId3e101f22c18d415bad8e179a84f6183e的图形的序号是________
说明: figure
6 . 如图所示,矩形eqId5ce7a06ae7a34393b92b5277978ac014和矩形eqId6f8a491b1fab4e30b2469bd099590893中,eqId21520e2eee634e05b9545889cc5d765e,点MN分别位于eqId437745e0711041d6b6502c50984428a3上,且eqIdbd18ed55ea1242cc837c91c0960a1326,矩形eqId6f8a491b1fab4e30b2469bd099590893可沿eqId99a3187c2b8f4bcc9703c74c3b72f1f3任意翻折.
说明: figure
(1)求证:当FAD不共线时,线段eqId876037be016c4316885be871978f005b总平行于平面eqId88c01382c3c34f3299f356b7e8475d37
(2)“不管怎样翻折矩形eqId6f8a491b1fab4e30b2469bd099590893,线段eqId876037be016c4316885be871978f005b总和线段eqId9b1f9f5244484dd19fa5c0cb4237c8e9平行,”这个结论对吗?如果对,请证明;如果不对,请说明能否改变个别已知条件使上述结论成立.
7 . 如图,已知正方形eqId5ce7a06ae7a34393b92b5277978ac014和矩形eqIdc0c84a4ae78b47f9a55dc30a007f7ef9所在的平面互相垂直,eqIdb60bb1649c8b41cb935771acc097167eeqId5380a0ee658b4ab8ba7b053286b6bbfdeqId2381423d4cd146cab95f55527681a766eqId1a0830891ff846de8422ea80714ecab4的中点.求证:
说明: figure
(1)平面eqIda3bba59055b84ba9b165f6555c0b0ee7平面eqId3f4717ddfa2d48fca27256eaa4e6a803
(2)eqId577d54bce5e84bfeabaeaeb481fefc71平面eqId076f835a1f2c428898c79204bd1d52fd
(3)eqId9bc4e9bcc8ae4bf99e7461793883794c平面eqId5968995e13a149e5b669a8baaeb00fab.
解答题 | 较易(0.85) | 2021·全国高一课时练习
同步
8 . 如图所示,在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqId2efda802d5534f6d92d9f8af7aaec28b为底面eqId5ce7a06ae7a34393b92b5277978ac014的中心,eqIdbedf755e0fdb4d078d6859360706b163eqIde4682078ddd9488281e376503edb4f95的中点,设eqId75a143b898e14ccdb032561fba9da811eqId8f39d706a505485987ccbb3f6177d72d上的点,问:当点eqId75a143b898e14ccdb032561fba9da811在什么位置时,平面eqIdf35ae9fe374c4039879b74caf6f5bfe1平面eqId94c05580372343acb27c5b0ecb094951
说明: figure
9 . 如图,在三棱锥eqId12175c05cfe240a0b8270ee03df1962f中,eqId312ef2c826304089b9b0f1d1e88b0f50eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175分别是eqIdd3a908032e2b40df95a6d86089b3f682eqId0fd9ac73d66042c6bbd74f8ccdcbd9fceqIdb53b60c33a254a27b9bfd58e818cc7e6的中点.eqId2381423d4cd146cab95f55527681a766eqId99a3187c2b8f4bcc9703c74c3b72f1f3上一点,连接eqId92b35bc1ddaa41adaa9027ab3cb1c2c9eqId517584fed25c413ba8b7bb33ffa2d5c6eqId47a318d9b1764ea2a94d27059e48c3a6eqId66d409c343f04cfda647f9bfc7da6b2a的交点,连接eqId81e750f39ba042b8a36a0f627f46b903,求证:eqId82872de12f654a5f9cdbd856fbb5f40d
说明: figure
填空题 | 一般(0.65) | 2021·全国
10 . 如图,在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175eqId92869ac114124367b45f631d030ed6bdeqId8846d653e4404636a88754285c8bcb32分别是棱eqId8f39d706a505485987ccbb3f6177d72deqId3549028b0a264a919e61d7f350198187eqIdb8aedba164b9446a81a96b5f315f00d0eqId34c6b6e427744abfb88dc90b8c7c2111的中点,eqId517584fed25c413ba8b7bb33ffa2d5c6eqId0627be51821d4be7b3e024a354815d64的中点,点eqId2381423d4cd146cab95f55527681a766在四边形eqIde275f19855c14957bc9a8147322beebe及其内部运动,则eqId2381423d4cd146cab95f55527681a766满足________时,有eqIde07a77ee3f8b413d8489cb5b09ab88db平面eqIda8872d39cdde4582870cc1afadc513d5
说明: figure