∴∠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.