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 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. 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. Neither is correct; the triangles are congruent by Side-Side-Angle. Neither is correct; the triangles are congruent by Side-Side-Angle. Neither is correct; the triangles are congruent by Side-Angle-Side. Neither is correct; the triangles are congruent by Side-Angle-Side.

Answer 1

To solve the problem, we need to analyze the information given and apply our understanding of triangle congruence.

1. We have two right triangles: △ABC (with right angle at B) and △PQR (with right angle at Q).
2. We're told that AB ≅ QR and AC ≅ PR.
3. Marcus claims that these triangles are congruent by the HL (Hypotenuse-Leg) Congruence Theorem.

The HL Congruence Theorem states that two right triangles are congruent if the length of the hypotenuse and one leg of one triangle are congruent to the length of the hypotenuse and one leg of the other triangle.

In the case of triangle △ABC:

• AB is one leg.
• AC is the hypotenuse.

In the case of triangle △PQR:

• QR is one leg.
• PR is the hypotenuse.

However, we do not have information about the length of the other leg (BC and PQ), which is important in establishing congruence.

Marlee's point about the corresponding legs not being marked as congruent is valid because, without knowing the equality of the other legs, we cannot conclude congruence through the HL theorem.

Thus:

• Since there is no information provided that confirms the angles or the lengths of the legs BC and PQ, we cannot definitively prove that the triangles are congruent based solely on the given information.

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