if a b, which of the following relationship can be proved and why?

Answer:
A) ΔACD ≅ ΔBCD because of AAS
Step-by-step explanation:
You are given ∠A ≅ ∠B. The diagram tells you the angles at C are congruent (both are right angles). You know side CD is congruent to itself.
The corrsponding side is not found between the corresponding angles, so you have enough information to invoke the AAS congruence theorem.