To determine the correct reasoning behind the congruence of triangles ABC and PQR based on the provided congruences and angles, let's analyze the information given.
- Triangle ABC has a right angle at B, and Triangle PQR has a right angle at Q.
- We know that \( \overline{AB} \cong \overline{QR} \) and \( \overline{AC} \cong \overline{PR} \).
Wyatt's Argument:
- Wyatt claims the triangles are congruent by the HL (Hypotenuse-Leg) Congruence Theorem. The HL Theorem states that in two right triangles, if the length of the hypotenuse and one leg are equal, then the triangles are congruent.
- In order for Wyatt to be correct, we would need to know that \( \overline{BC} \cong \overline{RQ} \) (the other leg). This information is not provided.
Parker's Argument:
- Parker claims the triangles are congruent by SAS (Side-Angle-Side) Theorem. To apply SAS, we would need two sides and the included angle to be congruent.
- However, since the angles and the sides presented do not form a complete set for SAS (the included angle is not between the two congruent sides), Parker’s argument does not hold with the given information.
Conclusion:
Given that the information provided does not support either the HL theorem (because the third leg is not compared) or SAS (because the angle isn't between both sides compared), it leads us to the right conclusion.
Therefore, the correct answer is: Both are wrong, the triangles are not congruent.