Question

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¯¯¯¯¯¯¯¯ . 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 Parker is correct Parker 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

Answer 1

To determine who is correct, let's analyze the information given:

1. Triangle ABC has a right angle at B, and triangle PQR has a right angle at Q.
2. The corresponding sides are as follows:
   • AB ≅ QR
   • AC ≅ PR

Wyatt claims that the triangles are congruent by the HL (Hypotenuse-Leg) Congruence Theorem. The HL Congruence Theorem states that if you have a right triangle, and you know the lengths of the hypotenuse and one leg, then the two right triangles are congruent.

In triangle ABC, we have:

• The hypotenuse would be the side opposite the right angle (which is not specified but can be inferred).
• The leg AB and the leg AC are given congruences.

Parker thinks they are congruent by SAS (Side-Angle-Side). For SAS, you need two sides and the angle between them, which also seems applicable since angle B (90 degrees) is between sides AB and AC.

Since both triangles are right triangles:

• Wyatt is correct in stating that they can be proven congruent by the HL theorem using AB and AC.
• Parker is also correct as SAS could work because they have two sides (AB and AC) and the included angle (90 degrees).

Therefore, since both methods validate the congruence of the triangles, the correct response would be that both Wyatt and Parker are correct.

So the best response is: Both are correct.