Question

如图所示,在四边形ABCD中,角A=角C=90度,BE平分角ABC,DF平分角ADC,BE与DF有什么位置关系?

Answer 1

四边形的内角和=(4-2)*180=360.则∠abc+∠cda=360-(90+90)=180.∠abc=2∠abe,∠cda=2∠cdf.∴2(∠abe+∠cdf)=180,
∠abe+∠cdf=90.又∵∠abe+aeb=90，∴∠cdf=∠aeb。又∵∠adf=∠cdf(df是角平分线).∴∠aeb=∠adf，从而be//df(同位角相等，二直线平行)