∵△ABC是等边三角形,∠DAE=120°,∴∠DAB+∠CAE=60°,∵∠ABC是△ABD的外角,∴∠DAB+∠D=∠ABC=60°,∴∠CAE=∠D,∵∠ABC=∠ACB=60°,∴∠ABD=∠ACE=120°,∴△ABD∽△ECA； （2）∵△ABD∽△ECA,∴ AB CE = BD AC ,即ABAC=BDCE,∵AB=AC=BC,∴BC2=BDCE．