线面平行、面面平行的证明问题思想方法归纳
1、四棱锥P-ABCD中，E.F分别在PA和BD 上且PE:EA=BF:FD=2:3。求证：EF//平面PBC。
![](https://wkrtcs.bdimg.com/rtcs/image?w=365.33&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_4","w":"365.33","h":"242.67","dataType":"gif","c":"word/media/image1.gif"})
（用两种方法，并写出详细证明过程）
![](https://wkrtcs.bdimg.com/rtcs/image?w=164.60&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_5","w":"164.60","h":"120.40","dataType":"png","c":"word/media/image2.png","imgOriW":365,"imgOriH":267})
方法一： 方法二：
以下第2-4题分别在相应图形中作出需要的辅助线，并简要写出证明思路即可
2. ![](https://wkrtcs.bdimg.com/rtcs/image?w=666.67&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_3","w":"666.67","h":"185.33","dataType":"gif","c":"word/media/image3.gif"})
以下两个四棱锥中，M.N分别为中点，分别求证：MN//平面PAD。
3. 四棱锥中,F.E为中点，求证AF//平面PEC 4.三棱柱中，D为中点，求证AC1//平面B1DC
![](https://wkrtcs.bdimg.com/rtcs/image?w=518.67&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_2","w":"518.67","h":"165.33","dataType":"gif","c":"word/media/image4.gif"})
5.在四棱锥中,M为中点。在MD上取点G，过AP和G作平面交平面BDM于GH。求证：AP//GH （写出详细证明过程）
![](https://wkrtcs.bdimg.com/rtcs/image?w=167.20&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_3","w":"167.20","h":"150.40","dataType":"png","c":"word/media/image5.png","imgOriW":209,"imgOriH":188})
练习1：正方体中，P.Q是中点。
（1）求证：PQ//平面DCC1D1 （2）求异面直线PQ和AB所成角的大小。
![](https://wkrtcs.bdimg.com/rtcs/image?w=172.00&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_4","w":"172.00","h":"172.00","dataType":"png","c":"word/media/image6_1.png","imgOriW":252,"imgOriH":253})
练习2：已知有公共边AB的两个全等的矩形ABCD和ABEF不在同一个平面内，P、Q分别是对角线AE、BD上的点，且AP=DQ。求证：PQ//![](https://wkrtcs.bdimg.com/rtcs/image?w=2.00&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_9","w":"2.00","h":"2.00","dataType":"png","c":"word/media/image7.png","imgOriW":5,"imgOriH":5})
平面CBE。 (用两种方法）
![](https://wkrtcs.bdimg.com/rtcs/image?w=264.00&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_2","w":"264.00","h":"157.33","dataType":"gif","c":"word/media/image8.gif"})
练习3．如图，四面体A-BCD被一个平面所截，截面EFGH是一个矩形。
（1）求证：CD//平面EFGH （2）求异面直线AB.CD所成的角。
![](https://wkrtcs.bdimg.com/rtcs/image?w=204.00&md5sum=82071df99e068d2e6d80de46fa2dd66a&sign=2ddbbf725c&rtcs_flag=2&rtcs_ver=4&l=webapp&bucketNum=261&ipr={"t":"img","r":"r_2","w":"204.00","h":"194.67","dataType":"gif","c":"word/media/image9.gif"})
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