In the scenario you described, both Wyatt and Parker are attempting to apply different congruence theorems to determine the congruence of triangles ABC and PQR.
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Wyatt's Argument (HL Congruence Theorem): The Hypotenuse-Leg (HL) theorem states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent. In this case, since <B and <Q are right angles and they know that AB = QR and AC = PR, it implies that A must be the hypotenuse for triangle ABC if they are using the right angle sides as legs. Therefore, they can't conclude congruence using HL because they need to confirm which sides correspond as the hypotenuse.
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Parker's Argument (SAS): The Side-Angle-Side (SAS) criterion states that two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle. However, in this case, while Parker correctly identifies the right angle as the included angle, it needs to be verified that the sides adjacent to that angle correspond correctly.
Since both arguments miss confirming the necessary conditions needed for HL and SAS properly, the triangles cannot be concluded as being congruent based solely on the information provided.
The correct conclusion in this case is: Both are wrong; the triangles are not necessarily congruent based on the information provided.
Thus, the answer is: Both are wrong; the triangles are not congruent.