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

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

Parker is correct
Parker is correct

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

Wyatt is correct

Answer 1

To determine whether Wyatt or Parker is correct regarding the congruence of triangles ABC and PQR, we need to analyze the information provided and the theorems they are referencing.

1. Wyatt says the triangles are congruent by the HL Congruence Theorem: The Hypotenuse-Leg (HL) Congruence Theorem applies only to right triangles. It states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. In this case, since both triangles are right triangles with one leg (AB ≅ QR) and another leg (AC ≅ PR), Wyatt is using the HL theorem appropriately.

2. Parker thinks they are congruent by SAS: The Side-Angle-Side (SAS) Congruence Theorem 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. However, in this case, they only have two sides of the triangles congruent and the right angle, but the “included angle” aspect does not apply since the angle between AB and AC in triangle ABC is not specifically the included angle for the sides they are measuring. Therefore, Parker is not correctly applying VBA.

Given that both ΔABC and ΔPQR are right triangles and that they satisfy the HL condition (one leg and the hypotenuse), Wyatt is correct in stating that they are congruent by the HL Congruence Theorem.

So, the correct response is: Wyatt is correct.