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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 CHoose the correct answer carefully and tell me why that is correct by using your context clues be smart

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

1 answer

To determine whether Wyatt or Parker is correct in their assertion about the congruence of triangles ABC and PQR, let's analyze the information given and the criteria for triangle congruence.

  1. Right Angles: Both triangles have a right angle:

    • Triangle ABC: ∠B = 90°
    • Triangle PQR: ∠Q = 90°

  2. Sides: We know that:

    • \( AB \cong QR \)
    • \( AC \cong PR \)

Now, let's evaluate the two arguments:

  • Wyatt's Argument (HL Congruence Theorem): The Hypotenuse-Leg congruence theorem states that for right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the triangles are congruent. Here, we have two legs (AB and AC) being compared to two sides of triangle PQR (QR and PR). We do not have the hypotenuses being mentioned in the information given, so this does not apply directly here.

  • Parker's Argument (SAS Congruence Theorem): The Side-Angle-Side theorem states that if two sides and the included angle of one triangle are congruent to the two sides and included angle of another triangle, then the triangles are congruent. However, in this case, the given information does not provide the measures of any angles besides the right angles.

Since we are comparing two right triangles with one leg and the hypotenuse (if we consider the right angles as the angle), we cannot classify this setup as SAS based solely on the provided information.

Conclusion: As neither Wyatt's use of the HL theorem nor Parker's use of the SAS theorem is applicable to the given information (especially because we're not explicitly comparing the hypotenuses), the most accurate response is:

Both are wrong, the triangles are not congruent.

So, the correct answer is: "Both are wrong, the triangles are not congruent."