Marcus and Marlee are comparing triangle ABC with right angle B with triangle PQR with right angle q to determine if they are congruent. line ab= line qr and line ac = line pr. Marcus says the triangles are congruent y the HL congruence theorem, but Marlee does not agree. who is correct?

Question

A. Marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent
B. neither is correct; the triangles are congruent by side-angle-side
C. 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
D. neither is correct; the triangles are congruent by side-side-angle

Answer 1

To determine the correct answer, we should evaluate the information provided.

1. Triangles ABC and PQR are both right triangles, meaning that we have a right angle in each triangle.
2. It's stated that \( AB = QR \) and \( AC = PR \), which correspond to one leg and the hypotenuse of each triangle, respectively.

The Hypotenuse-Leg (HL) Congruence Theorem states: If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Given that:

• \( AB \) (leg) corresponds with \( QR \) (leg).
• \( AC \) (hypotenuse) corresponds with \( PR \) (hypotenuse).

Conclusion: Marcus is correct; because both the hypotenuse and one leg of each triangle are congruent. Therefore, the triangles can be concluded as congruent via the HL theorem.

Thus, the correct answer is: C. 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.