Question

Based only on the facts in the diagram, which triangle criterion can you use to prove that ΔABC and ΔABD are congruent?

Answer 1

SAS, because it has two sides and an included angle. 

Answer 2

Based only on the facts in the diagram, you can see that:

1. BC≅BD (given);
2. ∠ABC is right, ∠ABD is also right, because these two angles are supplementary and together form the straight angle;
3. 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.

Answer: correct choice is A.