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: 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.

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.

Answer 1

Statement: ∠A ≅ ∠Q.

Reason: Third-Angle Theorem (if two angles of one triangle are congruent to two angles of another, the third angles are congruent).

Nessa's ASA proof used ∠B, ∠C and side BC; Roberto's AAS proof needs ∠A ≅ ∠Q to have two angles and a nonincluded side.