Wyatt and Parker are comparing two triangles to determine if they are congruent. For triangle ABC, <B measures 90 degrees and for triangle PQR, <Q is a right angle. They also know that AB¯¯¯¯¯¯¯¯ ≅QR¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯ ≅ PR¯¯¯¯¯¯¯¯

Question

. Wyatt says the triangles are congruent by the HL Congruence Theorem and Parker thinks that they are congruent by SAS. Who is correct? (Hint: Draw a picture)(1 point)
Responses A B C OR D WHICH ONE IS IT OR ILL KILL YOU

Both are wrong, the triangles are congruent by SSA
Both are wrong, the triangles are congruent by SSA

Parker is correct
Parker is correct

Wyatt is correct
Wyatt is correct

Both are wrong, the triangles are not congruent
Both are wrong, the triangles are not congruent

Answer 1

To determine which statement is correct, let's analyze the given information about the triangles ABC and PQR.

1. Triangle ABC has:

   • <B = 90 degrees (right angle)
   • Sides AB and AC are known sides.

2. Triangle PQR has:

   • <Q = 90 degrees (right angle)
   • Side QR is congruent to side AB, and side PR is congruent to side AC.

Given this information:

• Wyatt’s claim: He states the triangles are congruent by the HL (Hypotenuse-Leg) Congruence Theorem. The HL theorem applies specifically to right triangles, stating that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. In this case, you have two right triangles, but we do not have information about the hypotenuses directly. Instead, we only know the lengths of the legs, which would not be enough information to conclude with HL as we have no information about hypotenuses.

• Parker’s claim: He states the triangles are congruent by SAS (Side-Angle-Side) postulate. The SAS postulate 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. In this case, both triangles have a right angle included between the two pairs of sides that are known to be congruent (AB ≅ QR and AC ≅ PR).

Since both triangles have a right angle, and we know two pairs of sides are congruent, Parker's reasoning fulfills the requirement for the SAS congruence criterion.

Therefore, the correct response is:

Parker is correct.