Question

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.
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: AngleB ≅ AngleN; BC ≅ NM; AngleC is right; AngleM is right
Prove: TriangleABC ≅ TriangleQNM

AngleA ≅ AngleQ because of the third angle theorem.
AB ≅ QN because they are both opposite a right angle.
BC ≅ NM because it is given.
AngleC ≅ AngleM because right angles are congruent.

Answer 1

"∠A ≅ ∠Q" with reason "Third Angle Theorem (if two angles of one triangle are congruent to two angles of another, the third angles are congruent)."

Roberto needs this extra angle congruence to use AAS; Nessa's ASA proof did not require explicitly stating the third angle.