Question

如图,在等腰三角形ABC中,AB=AC,AB>BC.点D在边BC上.CD=2BD点E，F在线段AD上。∠1=∠2=∠BAC。若三角形ABC

面积为9，求△ABE与△CDF面积之和

Answer 1

∵∠1=∠BAC
∠1=∠BAD+∠ABE
∠BAC=∠BAD+∠CAF
∴∠ABE=∠CAF
同理∠BAD=∠ACF
∵AB=AC
∴⊿ABE≌⊿ACF(ASA)
∴S⊿ABE=S⊿ACF
∴△ABE与△CDF面积之和
=S⊿ACF+S⊿CDF
=S⊿ACD
=2／3S⊿ABC ﹙∵CD=2BD ∴CD=2／3BC﹚
=2／3×9
=6