Marcus and Marlee are comparing △ABC △ 𝐴 𝐵 𝐶 with right angle B 𝐵 with △PQR △ 𝑃 𝑄 𝑅 with right angle Q 𝑄 to determine if they are congruent. AB¯¯¯¯¯¯¯¯ ≅ QR¯¯¯¯¯¯¯¯ 𝐴 𝐵 ¯ ≅ 𝑄 𝑅 ¯ and AC¯¯¯¯¯¯¯¯ ≅ PR¯¯¯¯¯¯¯¯ 𝐴 𝐶 ¯ ≅ 𝑃 𝑅 ¯ . Marcus says the triangles are congruent by the HL Congruence Theorem, but Marlee does not agree. Who is correct? (Hint: Draw a picture.)(1 point) Responses Neither is correct; the triangles are congruent by Side-Side-Angle. Neither is correct; the triangles are congruent by Side-Side-Angle. Marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent. Marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent. Marcus is correct; the triangles are right triangles where a leg and the hypotenuse of one triangle is congruent to a leg and hypotenuse of the other triangle. Marcus is corre

Question

Marcus and Marlee are comparing △ABC △ 𝐴 𝐵 𝐶 with right angle B 𝐵 with △PQR △ 𝑃 𝑄 𝑅 with right angle Q 𝑄 to determine if they are congruent. AB¯¯¯¯¯¯¯¯ ≅ QR¯¯¯¯¯¯¯¯ 𝐴 𝐵 ¯ ≅ 𝑄 𝑅 ¯ and AC¯¯¯¯¯¯¯¯ ≅ PR¯¯¯¯¯¯¯¯ 𝐴 𝐶 ¯ ≅ 𝑃 𝑅 ¯ . Marcus says the triangles are congruent by the HL Congruence Theorem, but Marlee does not agree. Who is correct? (Hint: Draw a picture.)(1 point) Responses Neither is correct; the triangles are congruent by Side-Side-Angle. Neither is correct; the triangles are congruent by Side-Side-Angle. Marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent. Marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent. Marcus is correct; the triangles are right triangles where a leg and the hypotenuse of one triangle is congruent to a leg and hypotenuse of the other triangle. Marcus is corre

Answer 1

To determine the correct answer regarding the congruence of triangles \( \triangle ABC \) and \( \triangle PQR \), let's analyze the information provided and the reasoning behind the HL (Hypotenuse-Leg) Congruence Theorem.

Given:

\( \triangle ABC \) has a right angle at \( B \), and \( \triangle PQR \) has a right angle at \( Q \).
The sides are marked such that:
- \( \overline{AB} \cong \overline{QR} \)
- \( \overline{AC} \cong \overline{PR} \)

Marcus claims the triangles are congruent by the HL Theorem, which states that if in two right triangles the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle, then the triangles are congruent.

To apply the HL Theorem correctly, you need to ensure that:

The sides that correspond to the hypotenuse must indeed be the hypotenuses of their respective triangles.
The congruent leg must be one of the legs of the respective triangles.

However, Marlee argues that the triangles cannot be congruent because the corresponding legs are not marked as congruent.

Since the information does not specify that the legs opposite the right angles are congruent, Marlee is correct in pointing out that without this information, it cannot be confirmed that the triangles are congruent under the HL Theorem.

Therefore, the correct response is: Marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent.