Final answer:
Without additional context from the proofs mentioned, it's not possible to definitively choose which statement and reason would be unique to Roberto's proof. However, in general, the unique element could be the one involving a theorem or condition not used in the other proof.
Step-by-step explanation:
The question concerns which statement and reason would be unique to Roberto's proof that was not included in Nessa's proof when considering two geometric constructions or proofs involving triangles. Here we consider several mathematical statements:
- ZA = ZQ because of the third angle theorem.
- AB = QN because they are both opposite a right angle.
- BC = NM because it is given.
- ZC = ZM because right angles are congruent.
Without additional context, it's difficult to determine which statements and reasons are unique to Roberto's proof. However, if we assume that we are talking about two different proofs for congruent triangles, then the unique statement is likely the one that mentions a condition or a theorem not applied in Nessa's proof. The third angle theorem, for example, is applied when two angles in one triangle are known to be congruent to two angles in another triangle, which allows the conclusion that the third angles are also congruent. If this theorem wasn't used in Nessa's proof, it could be the unique statement for Roberto's proof with its corresponding reason.