Question

Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof?

Given: B ≅ N; BC ≅ NM; C is right; M is right
Prove: ABC ≅ QNM


A ≅ Q because of the third angle theorem.

AB ≅ QN because they are both opposite a right angle.

BC ≅ NM because it is given.

C ≅ M because right angles are congruent

Answer 1

In Roberto's proof, the statement and reason that would be included and not included in Nessa's proof are: C ≅ M because right angles are congruent.

Step-by-step explanation:

In Roberto's proof, the statement and reason that would be included and not included in Nessa's proof are:

1. Statement: C ≅ M
   Reason: Right angles are congruent

In Nessa's proof, she used the ASA (Angle-Side-Angle) congruence postulate to prove that the triangles are congruent. This means that she showed that two pairs of corresponding angles and the included side are congruent. In Roberto's proof, he used the AAS (Angle-Angle-Side) congruence postulate, which means he showed that two pairs of corresponding angles and a pair of corresponding sides are congruent. So adding the statement and reason mentioned above completes Roberto's proof.

Answer 2

A=Q Because of the third angle theorem