Question

如图,△abc中,ab=ac,∠dbc=∠ecb,ad:ac=1:4,s△dbc=10,求s△eac

Answer 1

∵AB=AC

∴∠ABC=∠ACB

∵∠DBC=∠ECB

∴∠ABD=∠ACE

又∵∠DAB=∠EAC,∠DAB=∠EAC

∴△ABD∽△ACE

∵AB=AC∴AB/AC=AD/AE=BD/EC=1

∴AD=AE,AB=AC,BD=EC

∴△ABD≌△ACE

∴S△BDC=S△EAC=10

∴S△EAC=10

(在这题目里ad:ac=1:4好像有点多余,请再次检查一下题目是否有误.)