To determine the correct congruence criterion for triangles ABC and PQR, let's analyze the information given:
- Both triangles have a right angle: ∠B = 90° and ∠Q = 90°.
- We know that AB ≅ QR and AC ≅ PR.
Wyatt's Claim (HL Congruence Theorem):
The Hypotenuse-Leg (HL) Congruence Theorem states that if we have two right triangles, and the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of the other triangle, the triangles are congruent. In this case, however, we are missing the information about the hypotenuses:
- It is unclear whether BC ≅ PQ (the hypotenuses).
Since the congruences given do not specify the hypotenuse, Wyatt is not correct in asserting convergence by the HL theorem alone.
Parker's Claim (SAS):
The Side-Angle-Side (SAS) Congruence Postulate states that if two sides and the angle between them in one triangle are equal to two sides and the included angle in another triangle, then the two triangles are congruent. Parker claims they are congruent by SAS, but we only have two sides and one right angle, not the included angle between the sides presented.
Thus, Parker’s statement needs clarification on whether the angle between the sides given is indeed 90 degrees.
Conclusion:
- Without knowing the length of the hypotenuses, we can’t assert congruence by the HL Theorem.
- SAS cannot be confirmed because we are uncertain that the angle between the two sides provided (AB and AC or QR and PR) is indeed right.
Given these points, both Wyatt and Parker are not correct in their assertions based on the given information.
The correct option is: Both are wrong, the triangles are not congruent.