1 如图，已知点![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"16","h":"17","dataType":"gif","c":"word/media/image1.png"})
是平行四边形所在平面外的一点，，分别是，上的点且，求证：平面．
![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"16","h":"77.333333333333","dataType":"gif","c":"word/media/image12.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=37.333333333333&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"37.333333333333","h":"74.666666666667","dataType":"gif","c":"word/media/image16.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=82.666666666667&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"82.666666666667","h":"46.666666666667","dataType":"gif","c":"word/media/image19.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=133.33333333333&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"133.33333333333","h":"1.3333333333333","dataType":"gif","c":"word/media/image25.png"})
2 如图，空间四边形![](https://wkrtcs.bdimg.com/rtcs/image?w=48&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"48","h":"19","dataType":"gif","c":"word/media/image2.png"})
,平行于与的截面分别交、、、于、、、．
求证：四边形![](https://wkrtcs.bdimg.com/rtcs/image?w=51&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"51","h":"19","dataType":"gif","c":"word/media/image34.png"})
为平行四边形；
![](https://wkrtcs.bdimg.com/rtcs/image?w=236&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"236","h":"206.66666666667","dataType":"gif","c":"word/media/image35.png"})
3 如图，![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"73","h":"21","dataType":"gif","c":"word/media/image36.png"})
，直线与分别交，，于点，，和点，，，
求证：![](https://wkrtcs.bdimg.com/rtcs/image?w=71&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"71","h":"41","dataType":"gif","c":"word/media/image46.png"})
．
![](https://wkrtcs.bdimg.com/rtcs/image?w=228&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"228","h":"274.66666666667","dataType":"gif","c":"word/media/image47.png"})
4 如图所示，在棱长为![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"13","h":"15","dataType":"gif","c":"word/media/image37.png"})
的正方体中，，，，分别是，，，的中点．
（1） 求证：![](https://wkrtcs.bdimg.com/rtcs/image?w=43&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"43","h":"23","dataType":"gif","c":"word/media/image52.png"})
平面．
（2） 求![](https://wkrtcs.bdimg.com/rtcs/image?w=27&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"27","h":"21","dataType":"gif","c":"word/media/image54.png"})
的长．
（3） 求证：![](https://wkrtcs.bdimg.com/rtcs/image?w=43&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"43","h":"20","dataType":"gif","c":"word/media/image55.png"})
平面．
![](https://wkrtcs.bdimg.com/rtcs/image?w=221&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"221","h":"217","dataType":"gif","c":"word/media/image57.png"})
5 如图，在正方体![](https://wkrtcs.bdimg.com/rtcs/image?w=119&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"119","h":"24","dataType":"gif","c":"word/media/image48.png"})
中，，，，分别棱是，，，的中点，是的中点，点在四边形及其内部运动，则满足 时，有平面．
![](https://wkrtcs.bdimg.com/rtcs/image?w=202.66666666667&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"202.66666666667","h":"200","dataType":"gif","c":"word/media/image65.png"})
6 如图，![](https://wkrtcs.bdimg.com/rtcs/image?w=21&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"21","h":"17","dataType":"gif","c":"word/media/image61.png"})
、、分别为空间四边形的边，，上的点，且．
求证：（１）![](https://wkrtcs.bdimg.com/rtcs/image?w=43&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"43","h":"20","dataType":"gif","c":"word/media/image68.png"})
平面，平面；
（２）平面![](https://wkrtcs.bdimg.com/rtcs/image?w=40&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"40","h":"19","dataType":"gif","c":"word/media/image69.png"})
与平面的交线．
7如图，在正方体中，求证：平面平面．
![](https://wkrtcs.bdimg.com/rtcs/image?w=249.33333333333&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"249.33333333333","h":"222.66666666667","dataType":"gif","c":"word/media/image75.png"})
8 图，在四棱锥![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"73","h":"19","dataType":"gif","c":"word/media/image76.png"})
中，是平行四边形，，分别是，的中点．
求证：![](https://wkrtcs.bdimg.com/rtcs/image?w=47&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"47","h":"20","dataType":"gif","c":"word/media/image63.png"})
平面．
![](https://wkrtcs.bdimg.com/rtcs/image?w=270.66666666667&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"270.66666666667","h":"230.66666666667","dataType":"gif","c":"word/media/image79.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=168&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"168","h":"144.66666666667","dataType":"png","c":"word/media/image80_1.png","imgOriW":209,"imgOriH":180})
9如图，正三棱柱的底面边长是2，侧棱长是，D是AC的中点.求证：平面.
10 .如图，在正四棱锥![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=864d0fb38677b3f5f5fe4164919135ea&sign=a6b5367e1c&rtcs_flag=1&rtcs_ver=3.7&l=webapp&bucketNum=44&ipr={"t":"img","w":"73","h":"19","dataType":"gif","c":"word/media/image86.png"})
中，,点在棱上． 问点在何处时，，并加以证明.
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