专题8.4直线、平面平行判定与性质讲-2016年高考数学文一轮复习讲练测解析版

第/r/n04/r/n 直线、平面平行的判定与性/r/n【课/r/n前/r/n小/r/n测/r/n摸/r/n底/r/n直线/r/na/r/n∥平面/r/nα/r/n，则/r/na/r/n平行于/r/n平面/r/nα/r/n内的/r/n /r/n /r/n /r/n【答案】/r/n【/r/n2015/r/n7/r/n】若/r/nl/r/nm/r/n/r/n是两条不同的直线，/r/nm/r/n/r/n垂直于平面/r/n/r/n/r/nl/r/n/r/n/r/nm/r/n/r/nl/r/n/r/n/r/n /r/n充分而/r/n不必要条件/r/n/r/nB/r/n．必/r/n要而不充/r/n分条件/r/n/r/nC/r/n．/r/n充分必要条/r/n /r/n【答案】/r/n【解析】若/r/nl/r/n/r/nm/r/nm/r/n垂直于平面/r/n/r/n，则/r/nl/r/n/r/n或/r/nl/r/n/r/n/r/n；若/r/nl/r/n/r/nm/r/n垂直于平面/r/n/r/n/r/n，则/r/nl/r/n/r/nm/r/nl/r/n/r/n/r/nm/r/n/r/nl/r/n/r/n/r/n(陕西省镇安中学/r/n2016/r/n届高三月考、理、/r/n9/r/n）/r/nl/r/nm/r/n及平面/r/n/r/n/r/n/r/n，下列说法中正确的是/r/n /r/nA．/r/n若/r/nl/r/n∥/r/n/r/n,/r/n/r/n/r/n/r/n/r/n/r/n/r/n/r/nm/r/n,/r/n则/r/nC．/r/n若/r/nl/r/n/r/n/r/n/r/n,/r/nl/r/n/r/n/r/n,则/r/n/r/n/r/n/r/n

/r/n /r/nB./r/n若/r/nl/r/n∥/r/n/r/n,/r/nm/r/n/r/n∥/r/n/r/n/r/n,则/r/nl/r/nD．/r/n若/r/nl/r/n∥/r/n/r/nl/r/nm/r/n，则/r/nm/r/n/r/n【答案】/r/n【/r/n解/r/n析/r/n】/r/nA，/r/n由/r/nl/r/n∥/r/n/r/n/r/n

/r/n/r/n/r/n/r/n是不能推出/r/nl/r/nm/r/n/r/n/r/n/r/n/r/n/r/n /r/n /r/n【/r/n2015·/r/n长沙模拟/r/n】若直线/r/na/r/n⊥/r/nb/r/n，/r/n且直线/r/na/r/n∥平面/r/nα/r/n，则直线/r/nb/r/n与平面/r/nα/r/n的/r/n位置关/r/n系是/r/n( /r/nC/r/n．/r/nb/r/n⊂/r/nα/r/nb/r/n∥/r/nα/r/nD/r/n．/r/nb/r/nα/r/nb/r/n⊂/r/nα/r/n【答案】/r/n【解析】/r/n/r/nb/r/nα/r/nb/r/n⊂/r/nα/r/nb/r/n∥/r/nα/r/na/r/n⊥/r/nb/r/na/r/n/r/nα/r/n【考/r/n点/r/n深/r/n度/r/n剖/r/n析/r/n【经/r/n典/r/n例/r/n题/r/n精/r/n析/r/n /r/n/r/nα/r/na/r/n，/r/nb/r/na/r/n，/r/nb/r/n的距离相等．/r/nA/r/n．①与/r/n /r/n /r/nD/r/n．②/r/n与/r/n[/r/n答案/r/n]/r/n /r/n面/r/nα/r/n，直线/r/nm/r/n⊥直线/r/nn/r/n，则直线/r/nn/r/n可能/r/n平行于平面/r/nα/r/n，/r/n也可能在平面/r/nα/r/n内，因/r/n此①③/r/n为假命题．/r/n/r/n/r/n/r/n/r/n /r/n【/r/n1-3/r/nα/r/n，/r/nβ/r/n，/r/nγ/r/n是三个不重合的平面，/r/na/r/n，/r/nb/r/n是两条不重合的直线，有下列三个条件：①/r/na/r/n∥/r/nγ/r/n，/r/nb/r/n/r/n///r/n②/r/na/r/n∥/r/nγ/r/n，/r/nb/r/n∥/r/nβ/r/n；③/r/nb/r/n∥/r/nβ/r/n，/r/na/r/n/r/n///r/nγ/r/n./r/n如果命题“/r/nα/r/n∩/r/nβ/r/n＝/r/na/r/n，/r/nb/r/n/r/n///r/nγ/r/n，且/r/n /r/n /r/nA/r/n．①或/r/n /r/n /r/nD/r/n．只有/r/n【答案】/r/n【解析】由定理“一条直线与一个平面平行，则过这条直线的任一平面与此平面的交线与该直线平行”/r/nC./r/n/r/nN/r/n是/r/nBC/r/n的中点，点/r/nM/r/n在四边形/r/nEFGH/r/n及其/r/n运动，则/r/nM/r/n满/r/n足条/r/n /r/n【答案】/r/nM/r/n/r/n段/r/nHF/r/n/r/nAB/r/n，/r/nBC/r/n，/r/nPD/r/n，/r/nPC/r/n的中点．/r/n (1)/r/n∵/r/nM/r/n、/r/nN/r/n为/r/nPD/r/n、/r/nPC/r/n的/r/n中点/r/n∴/r/nMN/r/n/r/nDC/r/n，又∵/r/nDC/r/n/r/n∴/r/nMN/r/n/r/n∥/r/n/r/n因为/r/nE/r/n为/r/nPB/r/n的中/r/n点，所以/r/n /r/n

/r/n

/r/nDCEH/r/n是平行四边形．/r/nCE/r/n/r/n∥/r/nDH/r/n./r/nCE/r/nPAD/r/n./r/n【/r/n回眸/r/n判定/r/n【/r/n方/r/n律技巧/r/n/r/n /r/nA/r/nm/r/n，/r/nn/r/nα/r/n【答案】/r/n/r/n【变式/r/n2】如图，正方体/r/nABCD/r/n－/r/nA/r/n1/r/nB/r/n1/r/nC/r/n1/r/nD/r/n1/r/n中，/r/nE/r/n、/r/nF/r/n分别为棱/r/nAB/r/n、/r/nCC/r/n1/r/n的中点，/r/n在平面/r/nADD/r/n1/r/nA/r/n1/r/n内且与/r/n平面/r/nD/r/n1/r/nEF/r/n平行/r/n的直线/r/n( /r/nA/r/n．不存/r/n /r/nB/r/n．有/r/n1/r/nC/r/n．有/r/n2/r/n /r/n /r/n/r/n件是/r/n /r/n /r/nC/r/n．/r/nAB/r/n与/r/nCD/r/n相/r/n /r/nD/r/n．/r/nA/r/n，/r/nB/r/n，/r/nC/r/n，/r/nD/r/n共/r/n【答案】/r/n/r/n/r/n/r/n＝/r/nBD/r/nα/r/n∥/r/nβ/r/nAC/r/n∥/r/nBD/r/n，故选/r/n/r/n /r/n /r/n /r/n【答案】/r/nl/r/n⊂/r/nα/r/n，/r/nm/r/n⊂/r/nβ/r/n，则/r/nl/r/n∥/r/nm/r/n；命题/r/nq/r/n：若/r/nl/r/n∥/r/nα/r/n，/r/nm/r/n⊥/r/nl/r/n，/r/nm/r/n⊂/r/nβ/r/n，则/r/nα/r/n⊥/r/nβ/r/n./r/n下/r/n列命题为/r/n真命题的是/r/n( /r/n /r/nC/r/n．/r/n(/r/n/r/n /r/nD/r/n．/r/np/r/n∧/r/n(/r/n/r/n【答案】/r/np/r/nm/r/n⊥/r/nl/r/n，/r/nl/r/n∥/r/nα/r/n时，/r/nm/r/n不一定/r/nα/r/n垂直，/r/nα/r/n⊥/r/nβ/r/nq/r/n也是假命题．/r/n/r/np/r/n)/r/n∨/r/nq/r/n【/r/n2-1/r/n【/r/n2015/r/n高考 ，理/r/n5/r/n】已/r/n知/r/nm/r/n，/r/nn/r/n是两条不同/r/n直/r/n线，/r/n/r/n，/r/n/r/n/r/n是两个不同平/r/n面，则下/r/n列命题正确/r/n的/r/n /r/n若/r/n/r/n/r/n垂直于同一平面，则/r/n/r/n/r/n若/r/nm/r/nn/r/n平行于同一平面，则/r/nm/r/n与/r/nn/r/n若/r/n/r/n/r/n不平行，则在/r/n/r/n/r/n若/r/nm/r/nn/r/n不平行，则/r/nm/r/nn/r/n【答案】/r/n【/r/n2-2/r/n【2015/r/n高/r/n考/r/n理/r/n4/r/n设/r/n/r/n，/r/n/r/n/r/n是两个不同的/r/n平面，/r/nm/r/n是直线/r/n且/r/nm/r/n⊂/r/n/r/n“/r/nm/r/n∥/r/n/r/n/r/n”/r/n是/r/n“/r/n/r/n∥/r/n/r/n/r/n”/r/n /r/n /r/n /r/n【答案】/r/n【解析】因为/r/n/r/n/r/n/r/n/r/nm/r/n/r/n是直线且/r/nm/r/n/r/n/r/n．若/r/nm/r/n∥/r/n/r/n/r/n”/r/n，则平面/r/n/r/n、/r/n/r/n/r/n平行，不能推出/r/n/r/n///r/n/r/n，反过来若/r/n/r/n///r/n/r/nm/r/n/r/n/r/n/r/n/r/n/r/n，则有/r/nm/r/n∥/r/n/r/n/r/n，则/r/nm/r/n∥/r/n/r/n/r/n”/r/n是/r/n“/r/n/r/n∥/r/n/r/n/r/n”/r/n条件/r/n /r/na/r/nα/r/nl/r/nα/r/nl/r/nα/r/nl/r/nα/r/nl/r/nα/r/nl/r/nα/r/n /r/n /r/n /r/n【答案】/r/n/r/n/r/n)/r/nA/r/n．/r/n3/r/n/r/nB/r/n．/r/n2/r/nC/r/n．/r/n1/r/nD/r/n．/r/n0/r/n/r/n /r/n /r/nD/r/n /r/n，/r/n斜/r/n三/r/n棱柱/r/nABC/r/n－/r/nA/r/n1/r/nB/r/n1/r/nC/r/n1/r/n中/r/n点/r/nD/r/n，/r/nD/r/n1/r/n分/r/n别/r/n为/r/nAC/r/n，/r/nA/r/n1/r/nC/r/n1/r/n上/r/n的/r/n点．(1)/r/nD/r/n1/r/n/r/n等/r/n于/r/n何/r/n值/r/n时，/r/nBC/r/n1/r/n∥/r/n平/r/n面/r/n/r/n(2)/r/nBC/r/n1/r/nD/r/nAB/r/n1/r/nD/r/n1/r/n，求的值．/r/n(2)/r/n由/r/n平/r/n面/r/nBC/r/n1/r/nD/r/n∥/r/n平/r/n面/r/nAB/r/n1/r/nD/r/n1/r/n，/r/n且/r/nA/r/n1/r/nBC/r/n1/r/n∩/r/n平/r/n面/r/nBC/r/n1/r/nD/r/n＝/r/nBC/r/n1/r/n，/r/n平/r/n面/r/nA/r/n1/r/nBC/r/n1/r/n∩/r/nAB/r/n1/r/nD/r/n1/r/n＝/r/nD/r/n1/r/nO/r/n /r/n∴/r/nD/r/nC/r/n＝/r/nOB/r/n1/r/n/r/n /r/n

/r/n

/r/n /r/n1/r/n1/r/n又由题可知/r/nD/r/nC/r/n＝/r/n/r/n1/r/n1/r/n

/r/n＝1，∴/r/n/r/n＝1，/r/n

/r/n【/r/n回眸/r/n/r/n/r/n/r/n/r/n /r/nA/r/n．/r/nm/r/n∥/r/nβ/r/n且/r/n /r/nB/r/n．/r/nm/r/n∥/r/nl/r/n1/r/n且/r/nm/r/n∥/r/nβ/r/n/r/n且/r/n /r/nD/r/n．/r/nm/r/n∥/r/nβ/r/n且/r/n【答案】/r/nA/r/nB/r/nl/r/n1/r/nl/r/n2/r/nl/r/n1/r/n∥/r/nm/r/nl/r/n1/r/n∥/r/nα/r/nl/r/n2/r/n∥/r/nα/r/nl/r/n1/r/nl/r/n2/r/nα/r/n∥/r/nβ/r/nα/r/n∥/r/nβ/r/nl/r/n1/r/n∥/r/nm/r/n，它们也可以异面，故必要/r/nB/r/nC/r/nm/r/n，/r/nn/r/n不一定相交，故是必要非充分条件；对于选项/r/nD/r/nn/r/n∥/r/nl/r/n2/r/n可转/r/n化为/r/nn/r/n∥/r/nβ/r/n，/r/nC，故不符合题意．/r/n【变式/r/n2/r/n【/r/n河北石家庄/r/n2014/r/n届/r/n高三调研/r/n试题】/r/n设/r/n/r/n表/r/n示直/r/n线/r/n/r/n,/r/n/r/n,/r/n/r/n表示不同的平/r/n面，则下/r/n列命题中/r/n正确/r/n /r/nA/r/n．/r/n若/r/na/r/n/r/n/r/n/r/n且/r/na/r/n/r/nb/r/n，/r/n则/r/nb/r/n//r/n /r/nB/r/n．/r/n若/r/n/r/n/r/n/r/n/r/n/r/n且/r/n/r/n/r/n/r/n/r/n/r/n/r/n，/r/n则/r/n/r/n/r/n//r/n//r/nC/r/n．若/r/na/r/n//r/n//r/n/r/n且/r/na/r/n//r/n//r/n/r/n/r/n，/r/n则/r/n/r/n/r/n//r/n//r/n /r/nD/r/n．/r/n若/r/n/r/n/r/n//r/n//r/n/r/n/r/n且/r/n/r/n/r/n//r/n//r/n/r/n/r/n，/r/n则/r/n/r/n/r/n//r/n//r/n【答案】/r/n【解析】A：应该/r/n是/r/nb/r/n///r/n/r/n/r/n或/r/nb/r/n/r/n/r/n/r/n；/r/nB/r/n：/r/n如果是墙角/r/n的三个面就不/r/n符合题意；/r/nC/r/n：/r/n/r/n /r/n/r/n/r/n/r/nm/r/n，/r/n若/r/na/r/n//r/n//r/nm/r/n时/r/n，满/r/n足/r/na/r/n///r/n/r/n/r/n，/r/na/r/n///r/n/r/n/r/n，但/r/n是/r/n/r/n/r/n///r/n/r/n/r/n不正确，所以/r/n选/r/nD./r/n/r/nA/r/n不/r/n在/r/n/r/n/r/n内，也不在/r/n/r/n/r/n内”是“过点/r/nA/r/n有且只有/r/n一条直线/r/n与/r/n/r/n/r/n和/r/n/r/n/r/n都平行”的（ /r/n/r/n /r/n /r/n /r/n【答案】/r/n4/r/nα/r/n∥/r/nβ/r/n∥/r/nγ/r/nl/r/n，/r/nm/r/nα/r/n，/r/nβ/r/n，/r/nγ/r/nA/r/n，/r/nB/r/n，/r/nC/r/n/r/nD/r/n，/r/nE/r/n，/r/nF/r/n /r/n【答案】/r/n

/r/n /r/n /r/n /r/n5/r/n】/r/n(2014·/r/n海淀区期末/r/n)/r/nABC/r/n－/r/nA/r/n1/r/nB/r/n1/r/nC/r/n1/r/n中，/r/nAA/r/n1/r/nABC/r/n，/r/nAB/r/n⊥/r/nAC/r/n，/r/nAC/r/n＝/r/nAA/r/n1/r/n，/r/nE/r/n，/r/nF/r/nBC/r/n，/r/nCC/r/n1/r/n的中点．/r/nAC/r/nD/r/nDEF/r/nABC/r/n1/r/nD/r/n (1)/r/n证明：∵/r/nA/r/n1/r/nA/r/n⊥底面/r/nABC/r/n，∴/r/nA/r/n1/r/nA/r/n⊥/r/nAB/r/n，/r/n∴/r/nAB/r/n∵在△/r/nABC/r/nE/r/nBC/r/n的中点，∴/r/nD/r/nAC/r/n/r/n/r/n /r/nA/r/n．/r/n若/r/na/r/n/r/n/r/n/r/n且/r/na/r/n/r/n/r/nb/r/n，/r/n则/r/nb/r/n//r/n /r/nB/r/n．/r/n若/r/n/r/n/r/n/r/n/r/n/r/n且/r/n/r/n/r/n/r/n/r/n/r/n/r/n，/r/n则/r/n/r/n/r/n//r/n//r/nC/r/n．若/r/na/r/n//r/n//r/n/r/n且/r/na/r/n//r/n//r/n/r/n/r/n，/r/n则/r/n/r/n/r/n//r/n//r/n /r/nD/r/n．/r/n若/r/n/r/n/r/n//r/n//r/n/r/n/r/n且/r/n/r/n/r/n//r/n//r/n/r/n/r/n，/r/n则/r/n/r/n/r/n//r/n//r/n【答案】/r/n/r/n /r/n/r/n/r/n/r/n/r/nm/r/n，/r/n若/r/na/r/n//r/n//r/nm/r/n时/r/n满足/r/na/r/n/r/na/r/n/r/n/r/n，但是/r/n/r/n/r/n/r/n/r/n不正确，所以选/r/n/r/n /r/n②/r/nAC/r/n1/r/n⊥平面/r/n/r/n③/r/nAC/r/n1/r/nABCD/r/n所成角的正切值是/r/n④/r/nCB/r/n1/r/nBD/r/n/r/n正切值是，故/r/n/r/n所成角/r/n /r/n/r/n正切值是，故/r/n2/r/n【3-3】/r/n已知平面/r/nα/r/n∥/r/nβ/r/n，/r/nP/r/n∉/r/nα/r/n且/r/nP/r/n∉/r/nβ/r/n，过点/r/nP/r/n的直线/r/nm/r/n与/r/nα/r/n，/r/nβ/r/n分别/r/n交于/r/nA/r/n./r/nC/r/n，过点/r/nP/r/n的直线/r/nn/r/n与/r/nα/r/n，/r/nβ/r/n分/r/n别/r/n交于/r/nB/r/n，/r/nD/r/n，且/r/nPA/r/n＝/r/n6/r/n，/r/nAC/r/n＝/r/n9/r/n，/r/nPD/r/n＝/r/n8/r/n则/r/nBD/r/n的长/r/n为/r/n /r/n5/r/nAC/r/nBD/r/n /r/n /r/n /r/n

/r/nBD/r/n/r/n

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/r/n＝/r/n5/r/n

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