如图在四边形abcd中,ab⊥bc,ad⊥dc,de⊥ac于e,交ab于f,求证△afd∽△adb

证明:∵∠AEF=∠ABC=90º;∠EAF=∠BAC.∴⊿EAF∽⊿BAC,AE/AB=AF/AC,AE*AC=AF*AB;同理可证:⊿AED∽⊿ADC,AE/AD=AD/AC,AE*AC=AD².∴AD²=AF*AB(等量代换),即AD/AF=AB/AD;又∠DAF=∠BAD(公共角相等).∴⊿A...