第/r/n04/r/n 直線、平面平行的判定與性/r/n【課/r/n前/r/n小/r/n測/r/n摸/r/n底/r/n直線/r/na/r/n∥平面/r/nα/r/n，則/r/na/r/n平行于/r/n平面/r/nα/r/n內的/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是兩條不同的直線，/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不必要條件/r/n/r/nB/r/n．必/r/n要而不充/r/n分條件/r/n/r/nC/r/n．/r/n充分必要條/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，則/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，則/r/nl/r/n/r/nm/r/nl/r/n/r/n/r/nm/r/n/r/nl/r/n/r/n/r/n(陜西省鎮安中學/r/n2016/r/n屆高三月考、理、/r/n9/r/n）/r/nl/r/nm/r/n及平面/r/n/r/n/r/n/r/n，下列說法中正確的是/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則/r/nC．/r/n若/r/nl/r/n/r/n/r/n/r/n,/r/nl/r/n/r/n/r/n,則/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,則/r/nl/r/nD．/r/n若/r/nl/r/n∥/r/n/r/nl/r/nm/r/n，則/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長沙模擬/r/n】若直線/r/na/r/n⊥/r/nb/r/n，/r/n且直線/r/na/r/n∥平面/r/nα/r/n，則直線/r/nb/r/n與平面/r/nα/r/n的/r/n位置關/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點/r/n深/r/n度/r/n剖/r/n析/r/n【經/r/n典/r/n例/r/n題/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的距離相等．/r/nA/r/n．①與/r/n /r/n /r/nD/r/n．②/r/n與/r/n[/r/n答案/r/n]/r/n /r/n面/r/nα/r/n，直線/r/nm/r/n⊥直線/r/nn/r/n，則直線/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內，因/r/n此①③/r/n為假命題．/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是三個不重合的平面，/r/na/r/n，/r/nb/r/n是兩條不重合的直線，有下列三個條件：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如果命題“/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“一條直線與一個平面平行，則過這條直線的任一平面與此平面的交線與該直線平行”/r/nC./r/n/r/nN/r/n是/r/nBC/r/n的中點，點/r/nM/r/n在四邊形/r/nEFGH/r/n及其/r/n運動，則/r/nM/r/n滿/r/n足條/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的中點．/r/n (1)/r/n∵/r/nM/r/n、/r/nN/r/n為/r/nPD/r/n、/r/nPC/r/n的/r/n中點/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因為/r/nE/r/n為/r/nPB/r/n的中/r/n點，所以/r/n /r/n

/r/n

/r/nDCEH/r/n是平行四邊形．/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【變式/r/n2】如圖，正方體/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分別為棱/r/nAB/r/n、/r/nCC/r/n1/r/n的中點，/r/n在平面/r/nADD/r/n1/r/nA/r/n1/r/n內且與/r/n平面/r/nD/r/n1/r/nEF/r/n平行/r/n的直線/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與/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，故選/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，則/r/nl/r/n∥/r/nm/r/n；命題/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，則/r/nα/r/n⊥/r/nβ/r/n./r/n下/r/n列命題為/r/n真命題的是/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時，/r/nm/r/n不一定/r/nα/r/n垂直，/r/nα/r/n⊥/r/nβ/r/nq/r/n也是假命題．/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是兩條不同/r/n直/r/n線，/r/n/r/n，/r/n/r/n/r/n是兩個不同平/r/n面，則下/r/n列命題正確/r/n的/r/n /r/n若/r/n/r/n/r/n垂直于同一平面，則/r/n/r/n/r/n若/r/nm/r/nn/r/n平行于同一平面，則/r/nm/r/n與/r/nn/r/n若/r/n/r/n/r/n不平行，則在/r/n/r/n/r/n若/r/nm/r/nn/r/n不平行，則/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設/r/n/r/n，/r/n/r/n/r/n是兩個不同的/r/n平面，/r/nm/r/n是直線/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】因為/r/n/r/n/r/n/r/n/r/nm/r/n/r/n是直線且/r/nm/r/n/r/n/r/n．若/r/nm/r/n∥/r/n/r/n/r/n”/r/n，則平面/r/n/r/n、/r/n/r/n/r/n平行，不能推出/r/n/r/n///r/n/r/n，反過來若/r/n/r/n///r/n/r/nm/r/n/r/n/r/n/r/n/r/n/r/n，則有/r/nm/r/n∥/r/n/r/n/r/n，則/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條件/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點/r/nD/r/n，/r/nD/r/n1/r/n分/r/n別/r/n為/r/nAC/r/n，/r/nA/r/n1/r/nC/r/n1/r/n上/r/n的/r/n點．(1)/r/nD/r/n1/r/n/r/n等/r/n于/r/n何/r/n值/r/n時，/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又由題可知/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，它們也可以異面，故必要/r/nB/r/nC/r/nm/r/n，/r/nn/r/n不一定相交，故是必要非充分條件；對于選項/r/nD/r/nn/r/n∥/r/nl/r/n2/r/n可轉/r/n化為/r/nn/r/n∥/r/nβ/r/n，/r/nC，故不符合題意．/r/n【變式/r/n2/r/n【/r/n河北石家莊/r/n2014/r/n屆/r/n高三調研/r/n試題】/r/n設/r/n/r/n表/r/n示直/r/n線/r/n/r/n,/r/n/r/n,/r/n/r/n表示不同的平/r/n面，則下/r/n列命題中/r/n正確/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則/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則/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則/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則/r/n/r/n/r/n//r/n//r/n【答案】/r/n【解析】A：應該/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如果是墻角/r/n的三個面就不/r/n符合題意；/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時/r/n，滿/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不正確，所以/r/n選/r/nD./r/n/r/nA/r/n不/r/n在/r/n/r/n/r/n內，也不在/r/n/r/n/r/n內”是“過點/r/nA/r/n有且只有/r/n一條直線/r/n與/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海淀區期末/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的中點．/r/nAC/r/nD/r/nDEF/r/nABC/r/n1/r/nD/r/n (1)/r/n證明：∵/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的中點，∴/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則/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則/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則/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則/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時/r/n滿足/r/na/r/n/r/na/r/n/r/n/r/n，但是/r/n/r/n/r/n/r/n/r/n不正確，所以選/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，過點/r/nP/r/n的直線/r/nm/r/n與/r/nα/r/n，/r/nβ/r/n分別/r/n交于/r/nA/r/n./r/nC/r/n，過點/r/nP/r/n的直線/r/nn/r/n與/r/nα/r/n，/r/nβ/r/n分/r/n別/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則/r/nBD/r/n的長/r/n為/r/n /r/n5/r/nAC/r/nBD/r/n /r/n /r/n /r/n

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

/r/n＝/r/n5/r/n /r/n /r/n /r/n∴/r/nPC/r/n＝/r/nPD/r/n，即/r/n3/r/n＝/r/n/r/n /r/n

/r/n＝/r/n5/r/n

/r/n/r/n/r/n/r/n/r/n(2)/r/n求/r/n證：平面/r/nA/r/n1/r/nBC/r/n⊥/r/n平面/r/nA/r/n1/r/nABB/r/n1/r/n./r/n (1)/r/n連接/r/nBC/r/n1/r/n，/r/nM/r/n，/r/nN/r/nA/r/n1/r/nC/r/n1/r/nA/r/n1/r/nB/r/n平面/r/n⊥平面/r/n【/r/n回眸/r/n判/r/n定/r/n定/r/n理/r/n：/r/na/r/n/r/nα/r/n，/r/nb/r/n/r/n/r/nα/r/n，/r/n且/r/n其他判定方法：/r/nα/r/n∥/r/nβ/r/n；/r/na/r/n/r/n直/r/n線/r/n和/r/n平/r/n面/r/n平/r/n行/r/n的/r/n性/r/n質/r/n定/r/n理：/r/na/r/n∥/r/nα/r/n，/r/na/r/n/r/n/r/n/r/n判/r/n定/r/n定/r/n理/r/n：/r/na/r/n/r/n/r/nα/r/n，/r/nb/r/n/r/n/r/n(1)/r/nα/r/n∥/r/nβ/r/n，/r/na/r/n/r/nα/r/n?/r/na/r/n∥/r/nβ/r/n；/r/n【/r/n方/r/n律/r/n技巧/r/n解決探究性問題/r/n一般要采用執/r/n果/r/n的方/r/n法，假設求/r/n解的結果存在，/r/n從這個結果出/r/n發，尋找使/r/n這個結/r/n現/r/n)，則/r/n不存在．/r/n1/r/nABCD/r/n－/r/nA/r/n1/r/nB/r/n1/r/nC/r/n1/r/nD/r/n1/r/n中，/r/nO/r/nABCD/r/n/r/n的中心，/r/nP/r/n/r/nDD/r/n1/r/nQ/r/n/r/n上的點，當點/r/nQ/r/n在/r/n /r/n）/r/n位/r/n置/r/n時，/r/n平/r/n面/r/nD/r/n1/r/nBQ/r/n∥/r/n平/r/n面/r/n/r/nA/r/n．/r/nQ/r/n/r/n與/r/nC/r/n重/r/n /r/nB/r/n．/r/nQ/r/n與/r/nC/r/n1/r/n重/r/nC/r/n．/r/nQ/r/n為/r/nCC/r/n1/r/n的三等/r/n分/r/n /r/nD/r/n．/r/nQ/r/n為/r/nCC/r/n1/r/n的/r/n中/r/n【答案】/r/n2/r/nABC/r/n－/r/nA/r/n1/r/nB/r/n1/r/nC/r/n1/r/n中，/r/nD/r/nBC/r/n的中點，/r/n求/r/n證/r/n：/r/nA/r/n1/r/nC/r/n∥/r/n平/r/n面/r/n/r/n/r/n/r/n∴/r/nE/r/n是/r/nA/r/n1/r/nB/r/n的中點，/r/n又∵/r/nD/r/nBC/r/n的中點，/r/n/r/n△/r/nA/r/nD/r/n|/r/nBB/r/n1/r/n|/r/n＝/r/n/r/n/r/n /r/n24/r/na/r/n/r/n【/r/n變/r/n式/r/n/r/n3/r/n】/r/n如/r/n圖，/r/n在/r/n四/r/n棱/r/n錐/r/n/r/nPABCD/r/n/r/n中/r/n，/r/n底/r/n面/r/n是/r/n平/r/n行/r/n四/r/n邊/r/n形/r/n，/r/nPA/r/n⊥/r/n平/r/n面/r/n/r/nABCD/r/n，/r/n點/r/n/r/nM/r/n、/r/nN/r/n/r/n分/r/n別/r/n為/r/n/r/nBC/r/n、/r/nPA/r/n/r/n的/r/n中/r/n點/r/n．/r/n段/r/nPD/r/n/r/n上/r/n是/r/n否/r/n存/r/n在/r/n一/r/n點/r/nE/r/n，使/r/nNM/r/n∥平面/r/nACE/r/n？/r/n若/r/n存/r/n在，/r/n請/r/n確/r/n定點/r/nE/r/n/r/n的/r/n位/r/n置/r/n；/r/n若/r/n不/r/n存/r/n在，請說/r/n明/r/n/r/nPD/r/nE/r/nNE/r/n，/r/nEC/r/n，/r/nAE/r/n，/r/nN/r/n，/r/nE/r/nPA/r/n，/r/nPD/r/nNE/r/n綉/r/n1/r/n又在平行四/r/n邊形/r/nABCD/r/n中，/r/nCM/r/n綉/r/n /r/n所以/r/nNE/r/n綉/r/nMC/r/n，即四邊形/r/nMCEN/r/n是平/r/n行四邊形．所以/r/nNM/r/n綉/r/nEC/r/n/r/nACE/r/n，/r/nNM/r/n?/r/nACE/r/nMN/r/nACE/r/n，/r/nPD/r/nE/r/nNM/r/nACE/r/n./r/n/r/n