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

Wyatt is correct
Wyatt is correct

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

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

Parker is correct

Answer 1

To determine who is correct between Wyatt and Parker regarding the congruence of triangles ABC and PQR, we need to analyze the information given and the congruence theorems involved.

We know:

1. Triangle ABC has a right angle at B.
2. Triangle PQR has a right angle at Q.
3. \( AB \cong QR \)
4. \( AC \cong PR \)

Wyatt is applying the HL (Hypotenuse-Leg) Congruence Theorem, which states that if you have a right triangle, the hypotenuse and one leg are congruent to those of another right triangle, then the triangles are congruent.

Parker is applying the SAS (Side-Angle-Side) Congruence Theorem, which 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.

Analyzing the statements:

• We have two right triangles, so we can apply HL.
• Since we know one leg (\(AB\) and \(QR\)) is congruent and the hypotenuse (\(AC\) and \(PR\)) is congruent, this situation satisfies the HL theorem.

Thus, Wyatt is correct. The triangles are congruent by HL. Parker's reasoning is not applicable here because he suggests using SAS, but we do not have information about the included angle between the two congruent sides we know.

Final answer: Wyatt is correct.