Given two right triangles $△abd$ and $△dca$, which congruency theorem can be used to prove that they are congruent? Choose from: $\text{SSS}$, $\text{ASA}$, $\text{SAS}$, or $\text{AAS}$.

• A. $\text{ASA}$
• B. $\text{AAS}$
• C. $\text{SAS}$
• D. $\text{SSS}$

Answer: (C)

Verified step by step guidance

1. Identify the two right triangles \( \triangle abd \) and \( \triangle dca \) and note that both have a right angle by definition.
2. Recall that in right triangles, one angle is 90 degrees, so this angle is congruent in both triangles.
3. Look for two other parts (sides or angles) that are congruent between the triangles. Since the right angle is known, if you can find one side adjacent to the right angle and the included angle or side between them, you can use the SAS (Side-Angle-Side) congruency theorem.
4. The SAS theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
5. Therefore, by identifying the right angle and the two corresponding sides that include this angle in both triangles, you can apply the SAS congruency theorem to prove the triangles are congruent.