There isn't enough info to prove the triangles to be congruent or not. So we can't say for sure either way.
We have angle CAD = angle ACB given by the arc markings, and we know that AC = AC due to the reflexive theorem. However we are missing one third piece of information.
That third piece of info could be....
- AD = BC which allows us to use SAS
- angle ACD = angle CAB which allows us to use ASA
- angle ABC = angle CDA which allows us to use AAS (slight variation of ASA)
Since we don't know any of those three facts, we simply don't have enough information.
side note: If AB = CD, then this leads to SSA which is not a valid congruence theorem. If we had two congruent sides, the angle must be between the two sides, which is what AD = BC allows.