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题型:解答题 难度系数:0.65 引用次数:116 更新时间:2019/01/11 05:40:46 题号:7447146
如图,已知,,,四边形是矩形,平面与平面垂直.为线段上一点.

(1)求证:
(2)若,求三棱锥的体积.
类题推荐
【推荐1】如图,在直角梯形eqId5ce7a06ae7a34393b92b5277978ac014中,eqId0d9961f0e84b4330a8b12a6efe4f3804,eqIdf635185beec44b6b86934e806f088b02, eqId18e3ae3e255349039d6726b8293c6cabeqIdded28dbc6ca54681ab966fe6545c6cdceqIdd9251115c9a9452088ecefa7fbb94bf8,点eqId93cbffaa5ae045d6ac45d1e979991c3aeqId34c6b6e427744abfb88dc90b8c7c2111上,且eqIdbae2ef596ca941b89c53f1059c2148aa,将eqId1ba8a6a849e04b31abd4a64a759061b5沿eqId7fd836b3d4ac4d398fb8e461e090364c折起,使得平面eqId0ab1105ccd73407e94304ecdd3826a0a平面eqId41b0fa6b45c44cf0aeaa1b53230916f1(如图),eqId92869ac114124367b45f631d030ed6bdeqId7fd836b3d4ac4d398fb8e461e090364c中点.
(Ⅰ)求证:eqId64d1930b6d2543918fe8f4cf888830c8平面eqId41b0fa6b45c44cf0aeaa1b53230916f1
(Ⅱ)求四棱锥eqIdade73050d9d84a649183fd4abf1227a9的体积;
(Ⅲ)在线段eqId1b51efe7c2fa42748ac5a6be262e2fa4上是否存在点eqIdd7be5abad1e34f6db17a56660de8d54f,使得eqId79bd4080945b4cba8e8cde7b608c5ac1平面eqId28f374605af2463f991d1dd23797fec1?若存在,求eqIdc02b3bc95ab346b89a60b73365aac0d3的值;若不存在,请说明理由.figure
难度系数:0.65使用:187次题型:解答题更新:2019/6/15
【推荐2】如图所示,正方体eqId588284d93dc5489295f8f224f8e30d13的棱长为1,eqId71891062a8724584af9a2c4c77cd566e为线段eqId0627be51821d4be7b3e024a354815d64eqId8f39d706a505485987ccbb3f6177d72d上的动点,过点eqId90f6330828254ae186021073d060ec28的平面截该正方体的截面记为S,则下列命题正确的是______
figure
①当eqId86c810f61b0e47f3931851148c159ac2eqId36befe82b46e4082ba6c49c494d476b4时,S为等腰梯形;
②当eqId71891062a8724584af9a2c4c77cd566e分别为eqId0627be51821d4be7b3e024a354815d64eqId8f39d706a505485987ccbb3f6177d72d的中点时,几何体eqId5453e2aecf564449889e81ee162858f5的体积为eqIdd056375c2cc745268c01dc2cbaa35258
③当M为eqId0627be51821d4be7b3e024a354815d64中点且eqId45a0a24cb68d41ada0742432320b13cf时,S与eqId3549028b0a264a919e61d7f350198187的交点为R,满足eqIdb64eaaa2dad64dde88c975c46973e3fc
④当M为eqId0627be51821d4be7b3e024a354815d64中点且eqId1e68f8169707452da440d442b3516fd0时,S为五边形;
⑤当eqIde0d882c16d6b48ad983cea20a60c672beqIda9689f21d41744b38c7fbbddf57da092时,S的面积eqIde0b8cd3018f64415bea8dce0a25d0538.
难度系数:0.4使用:8次题型:解答题更新:2019/6/27
【推荐3】如图,四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,平面eqId9174dc3b874545daa5de88a42acf01b3平面ABCDE为线段AD的中点,且eqIdedaaa7ba1b334787b9cd2efe681cb5f8eqIdcb00ed936fe94bb3aacf53fbc8ac2fb2eqIdfe1f79e3a4a54a0abec80086851983c7
figure
(1)证明:平面eqId8f39fd8e859642d3b91f860d274c0b85平面eqId1bf8da710ed845aaadfe28ce37f184f2
(2)若eqId5a61d30e33ed4e0cab8c0bb7e10c6a79,求三棱锥eqIdf5fd2c2abfdf40189ee6b7e996674ba0的体积.
难度系数:0.65使用:197次题型:解答题更新:2019/6/12
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