Question

if ∠deg ≅ ∠feg and dg = 82, what is fg?

Explanation:

Step1: Identify congruent - triangles concept

Since $\angle DEG\cong\angle FEG$, $EG = EG$ (common side), and $\angle EDG=\angle EFG = 90^{\circ}$, by the AAS (Angle - Angle - Side) congruence criterion, $\triangle DEG\cong\triangle FEG$.

Step2: Use congruent - triangle property

For congruent triangles $\triangle DEG$ and $\triangle FEG$, corresponding sides are equal. Given $DG$ and $FG$ are corresponding sides, and $DG = 82$, so $FG=82$.

Answer:

82