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

A=Q Because of the third angle theorem

Answer 2

From the given information,

B and C are extreme angles of BC and N and M are extreme angles of NM.

Also, it is given that B = N and C = M (= 90°) and BC ≅ NM.

With these details, Nessa used ASA congruent and proved that the triangles are congruent.

If we compare these statements with Roberto's proof,

AB ≅ QN is seen as an additional statement.

It seems that Roberto would miss the information BC ≅ NM. Otherwise, he also would go with ASA rule.

So, Roberto considered the statements B = N, C = M and AB ≅ QN and hence he opted AAS rule.