(2011•闵行区一模)已知:如图,在△ABC中,AB=AC,DE∥BC,点F在边AC上,DF与BE相交于点G,且∠EDF=∠ABE. 求证:(1)△DEF∽△BDE; (2)DG•DF=DB•EF.
问题描述:
(2011•闵行区一模)已知:如图,在△ABC中,AB=AC,DE∥BC,点F在边AC上,DF与BE相交于点G,且∠EDF=∠ABE.
求证:(1)△DEF∽△BDE;
(2)DG•DF=DB•EF.
答
证明:(1)∵AB=AC,∴∠ABC=∠ACB.(1分)∵DE∥BC,∴∠ABC+∠BDE=180°,∠ACB+∠CED=180°.(1分)∴∠BDE=∠CED.(1分)∵∠EDF=∠ABE,∴△DEF∽△BDE.(2分)(2)由△DEF∽△BDE,得DBDE=DEEF.(1分...