Question

Proof triangles

Answer 1

No, two sides the same is not enough.
You need more proof.

Side, angle, side. (SAS).
AD = DC
Angle ADB = Angle CDB
BD = BD

By the SAS property, the two triangles are the same.

I think this is one way to prove it...

Or, similarly...use ASA, (Angle, side, angle).