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 robertos proof that was not included in nessas proof? given: ∠b≅∠n; bc≅nm; ∠c is right; ∠m is right prove: △abc≅△qnm ∠a≅∠q because of the third - angle theorem. ∠c≅∠m because right angles are congruent. bc≅nm because it is given.

Explanation:

Nessa used ASA (Angle - Side - Angle) and Roberto used AAS (Angle - Angle - Side). In ASA, two angles and the included side are used for congruence. In AAS, two angles and a non - included side are used. Given the right angles and other equal angles and side, the third angle theorem result ($\angle A\cong\angle Q$) is needed for AAS but not for ASA where the other two angle - side combinations are sufficient.

Answer:

$\angle A\cong\angle Q$ because of the third angle theorem.