Select One

Question

Marcus and Marlee are comparing △ABC with right angle B with △PQR with right angle Q to determine if they are congruent. AB¯¯¯¯¯¯¯¯ ≅ QR¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯ ≅ PR¯¯¯¯¯¯¯¯ . 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-Angle-Side. Neither is correct; the triangles are congruent by Side-Angle-Side. 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 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. 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.

Answer 1

In this scenario, Marcus is correct. The HL (Hypotenuse-Leg) Congruence Theorem states that if you have two right triangles and you know that their hypotenuses and one pair of legs are congruent, then the triangles are congruent.

Here, we know that:

• \( AB \cong QR \) (one leg of triangle ABC is congruent to one leg of triangle PQR).
• \( AC \cong PR \) (the other leg of triangle ABC is congruent to the other leg of triangle PQR).

Since both triangles are right triangles and the congruence of the hypotenuses and a leg is established, the triangles are indeed congruent by the HL Congruence Theorem.

Therefore, the correct response is: 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.