As shown in the figure in abc,bc 120ad 60

(1) ∵ AB=BC, ∠ABC=120°,

∴∠A=∠C=30°,

∵AD=BD,

∴∠A=∠ABD=30°,

∴∠CBD=∠ABC-∠ABD=90°;

(2) △BDE is an equilateral triangle.

∵∠CBD=90°, ∠C=30°,

∴∠BDC=60°,

and E is the midpoint of DC,

∴BE=ED,

∴△BDE is an equilateral triangle.