平行线分线段成比例定理的证明过程
证明：过点A做直线AC//GN，如图所示，连接CD、BE，作BK⊥AC于K，CH⊥AB于H，
设直线DE和BC之间的距离为h,则：
![](https://wkrtcs.bdimg.com/rtcs/image?w=12&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"12","h":"22.666666666667","dataType":"gif","c":"word/media/image1.png"})
S△DBC=![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"16","h":"41.333333333333","dataType":"gif","c":"word/media/image4.png"})
BC·h=S△EBC（同底等高）
∵ S△ADC=S△ABC-S△DBC
S△AEB=S△ABC-S△EBC=S△ABC-S△DBC
![](https://wkrtcs.bdimg.com/rtcs/image?w=303&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"303","h":"264","dataType":"jpeg","c":"word/media/image5.png","imgOriW":303,"imgOriH":264})
∴ S△ADC=S△AEB
∴ ![](https://wkrtcs.bdimg.com/rtcs/image?w=100&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"100","h":"46.666666666667","dataType":"gif","c":"word/media/image6.png"})
∴ ![](https://wkrtcs.bdimg.com/rtcs/image?w=73.333333333333&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"73.333333333333","h":"41.333333333333","dataType":"gif","c":"word/media/image7.png"})
即：![](https://wkrtcs.bdimg.com/rtcs/image?w=146.66666666667&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"146.66666666667","h":"41.333333333333","dataType":"gif","c":"word/media/image8.png"})
即：![](https://wkrtcs.bdimg.com/rtcs/image?w=112&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"112","h":"41.333333333333","dataType":"gif","c":"word/media/image9.png"})
∴ ![](https://wkrtcs.bdimg.com/rtcs/image?w=72&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"72","h":"41.333333333333","dataType":"gif","c":"word/media/image10.png"})
即：![](https://wkrtcs.bdimg.com/rtcs/image?w=72&md5sum=2d8058e31300e7d653c4a74980557e65&sign=1396144a5d&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=27&ipr={"t":"img","w":"72","h":"41.333333333333","dataType":"gif","c":"word/media/image11.png"})
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