Which triangle criterion can you use to prove that ABC AND ABD are congruent?

Answer: Based only on the facts in the diagram, you can see that:
BC≅BD (given);
∠ABC is right, ∠ABD is also right, because these two angles are supplementary and together form the straight angle;
AB is common side.
You have two pairs of congruent sides and a pair of included congruent angles that are adjacent to the congruent sides. So you can use SAS Postulate correct choice is A. hope this answer helped you :)
Explanation: