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. ab ≅ qn because they are both opposite a right angle. bc ≅ nm because it is given. ∠c ≅ ∠m because right angles are congruent.

Explanation:

Nessa used ASA (Angle - Side - Angle) where two angles and the included side are congruent. Roberto used AAS (Angle - Angle - Side). To use AAS, he needed to show the third - pair of angles are congruent. Given two pairs of angles are congruent in right - triangles, the third pair of angles (the non - included angles for the given side) can be shown congruent using the third angle theorem.

Answer:

∠A ≅ ∠Q because of the third angle theorem.