To determine whether Marcus or Marlee is correct, let's carefully analyze the triangles AABC and APQR based on the information provided and the definitions of the congruence theorems.
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Review the Congruence Theorems:
- HL Congruence Theorem: States that if in two right triangles, the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the triangles are congruent.
- Side-Angle-Side (SAS): States that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
- Side-Side-Angle (SSA): States that two sides and a non-included angle are given, but this does not guarantee congruence.
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Analyze the Information:
- The triangles have given corresponding sides: AB = QR and AC = PR (as indicated by the statement).
- They are right triangles with right angles at B and Q.
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Evaluate Marcus' Claim:
- Marcus claims that the triangles are congruent by the HL theorem. For this to be true, we need to ensure that we have one leg and the hypotenuse of one triangle congruent to the leg and hypotenuse of the other triangle respectively.
- Without the additional mark on the legs (as Marlee implies), we cannot confirm that one leg of triangle AABC is congruent to the leg of triangle APQR.
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Evaluate Marlee's Claim:
- Marlee argues that the triangles are not congruent because the legs are not marked as congruent. This is valid; if the legs are not congruent, we cannot confidently say the triangles are congruent via HL.
Given this understanding and analysis, Marlee is correct. The triangles are not congruent because the corresponding legs are not marked as congruent.
Thus, the answer is: Marlee is correct, the triangles are not congruent because the corresponding legs are not marked as congruent.
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