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: angle cap b is congruent to angle cap n ; line segment cap b cap c is congruent to line segment cap n cap m ; angle cap c is right; angle cap m is right Prove: triangle cap A cap b cap c is congruent to triangle cap q cap n cap m

Nessa can use the given angles B and C (both right angles) with the given side BC, which lies between those angles, to prove congruence by ASA. For AAS, Roberto needs the angle at A instead of the angle at C: since angles B and N are congruent and angles C and M are congruent, the third angle theorem shows that angles A and Q are congruent. Then BC and NM are a non-included corresponding side, so the proof uses AAS.

AI-written and checked against the verified answer.