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

Parker is correct
Parker is correct

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

Wyatt is correct

Answer 1

To determine whether Wyatt or Parker is correct regarding the congruence of the two triangles, let's examine the information provided and the relevant congruence theorems:

1. Right Angle: Both triangles ABC and PQR have a right angle (∠B = 90° and ∠Q = 90°).
2. Congruent Sides: It's given that $AB\cong QR$ and $AC\cong PR$.

Now let's apply the two congruence theorems mentioned:

• HL Congruence Theorem: This theorem states that if a triangle has a right angle and the hypotenuse and one leg are congruent to the corresponding parts of another right triangle, then the triangles are congruent. In this case, it's not stated that $BC\cong PQ$ (the third side), which is necessary for applying the HL theorem. Therefore, without confirming that the lengths of the hypotenuses are equal as well, Wyatt cannot claim congruence through the HL theorem.

• SAS Congruence Theorem: This requires two sides and the included angle to be congruent. Though we have two congruent sides from the information provided, we lack information about the angle between them. Parker cannot confirm congruence through SAS without knowing an angle that is included between the two sides.

Since neither Wyatt nor Parker has enough information to definitively prove that the triangles are congruent through HL or SAS, the response that fits best is:

Both are wrong, the triangles are not congruent.

They don't have sufficient information regarding the third side or the included angle necessary for either theorem.