Question

what additional information is needed to prove that the triangles are congruent using the aas congruence theorem? ∠fgh≅∠kgj ∠gfh≅∠gkj (overline{gf}congoverline{gk}) (overline{hf}congoverline{jk})

Explanation:

Step1: Recall AAS congruence theorem

AAS (Angle - Angle - Side) requires two pairs of congruent angles and a non - included side congruent. We already have right angles $\angle FHG=\angle KJG = 90^{\circ}$ and $HG = GJ$ (from the markings).

Step2: Analyze the options

We need another pair of non - right angles to be congruent. $\angle GFH\cong\angle GKJ$ would give us the two angles and the non - included side ($HG = GJ$) for AAS.

Answer:

$\angle GFH\cong\angle GKJ$