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.

What would be included to prove both triangles are congruent by the AAS theorem is: B. AB ≅ QN because they are both opposite a right angle.

What is the AAS Congruence Theorem?

The AAS congruence theorem states that two triangle are congruent if both have two pairs of corresponding congruent angles and a pair of non-included corresponding congruent sides.

In the image given, since AB and QN both lie opposite a right triangle, then they are congruent to each other.

Therefore, to prove both triangles are congruent by AAS theorem, what would be included is: B. AB ≅ QN because they are both opposite a right angle.

Learn more about AAS congruence theorem on:

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