1. **State the problem:** We need to determine if triangles $\triangle COT$ and $\triangle NPA$ are congruent, and if so, by which rule. 2. **Given information:** - $\angle O$ and $\angle N$ are right angles. - Segment $TO$ is congruent to segment $NP$. - Segment $OC$ is congruent to segment $PA$. 3. **Identify the rule:** - Both triangles have a right angle, so $\angle O = \angle N = 90^\circ$. - Two pairs of corresponding sides are congruent: $TO \cong NP$ and $OC \cong PA$. - The right angle is between these two sides in each triangle. 4. **Apply the RHS (Right angle-Hypotenuse-Side) congruence rule:** - The right angle is given. - The hypotenuse $CT$ in $\triangle COT$ corresponds to $NA$ in $\triangle NPA$. - We need to check if the hypotenuses are congruent. Since the problem does not provide this, we cannot confirm RHS directly. 5. **Check for SAS (Side-Angle-Side) congruence:** - We have two sides and the included right angle. - Sides $TO$ and $NP$ are congruent. - Angles $O$ and $N$ are right angles. - Sides $OC$ and $PA$ are congruent. 6. **Conclusion:** - By SAS, $\triangle COT \cong \triangle NPA$. **Final answer:** $\triangle COT \cong \triangle NPA$ by SAS