(1)根据AB=AC,求得∠ABD=∠ACE,再利用AB
2=DB·CE,即可得出对应边成比例,然后即可证明.
(2)由△ADB∽△EAC,得出∠BAD=∠E,∠D=∠CAE,则∠DAE=∠BAD+∠BAC+∠CAE=∠D+∠BAD+∠BAC,很容易得出答案.
证明:(1)∵AB=AC,∴∠ABC=∠ACB,
∴∠ABD=∠ACE,
∵AB
2=DB·CE
∴
∴
∴△ADB∽△EAC.
(2)∵△ADB∽△EAC,∴∠BAD=∠E,∠D=∠CAE,
∵∠DAE=∠BAD+∠BAC+∠CAE,
∴∠DAE=∠D+∠BAD+∠BAC,
∵∠BAC=40°,AB=AC,
∴∠ABC=70°,
∴∠D+∠BAD=70°,
∴∠DAE=∠D+∠BAD+∠BAC=70°+40°=110°.