Question

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

A. SAS

B. SAA

C. ASA

D. SSS

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.