Solution: When (1)E is the midpoint of AB, the relationship between AE and DB is AE=DB.

The reasons are as follows: ∫△ABC is an equilateral triangle, and point E is the midpoint of AB.

∴ae=be； ∠BCE=30，

ED = EC，

∴∠ECD=∠D=30，

∫∠ABC = 60，

∴∠DEB=30，

∴db=be=ae；

(2)AE=DB .

As shown in figure 2, point E is EF∨BC, and point AC is point F,

∫EF∨BC，

∴∠AEF=∠ABC=60，∠AFE=∠ACB=60，

∫△AEF is an equilateral triangle, AE=EF=AF,

∴BE=CF，

ED = EC，

∴∠ECD=∠D，

And ≈ECF = 60-∠ECD, ∠ Debu = ∠ EBC-∠ D = 60-∠ D,

∴∠ECF=∠DEB，

∴△BDE≌△FEC,(SAS)

∴BD=EF=AE。