Question

In the figure below, ∠A≅∠DBE and AB≅BE. What additional information do you need in order to prove a pair of triangles congruent by AAS? please view picture

Answer 1

∠ACB ≅ ∠BDE

Explanation:

In ∆ ABC and ∆ BDE:

• ∠A ≅ ∠DBE (Given)
• AB ≅ BE (Given)

To prove these triangles congruent by AAS (Angle-Angle-Side), we need to establish that the angles ∠ACB and ∠BDE are congruent.

The additional information needed is ∠ACB ≅ ∠BDE.

With this additional information, we now have:

• ∠ACB ≅ ∠BDE (Additional Information)
• ∠A ≅ ∠DBE (Given)
• AB ≅ BE (Given)

Now, we have two pairs of congruent angles (∠A ≅ ∠DBE and ∠ACB ≅ ∠BDE) and one pair of congruent sides (AB ≅ BE).

By AAS, the triangles ABC and BDE are now proven to be congruent. The AAS congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

So, in summary, the additional information needed to prove the triangles congruent by AAS is ∠ACB ≅ ∠BDE.