Question

∠j ≅ ∠h and \\( \overline { h k } \cong \overline { g j } \\). complete the proof that \\( \delta f g j \cong \delta f k h \\).

Explanation:

Step1: Identify vertical angles

$\angle JIG \cong \angle HIF$ (Vertical angles are congruent)

Step2: Apply AAS congruence

$\triangle FGH \cong \triangle FKH$ (AAS: $\angle J \cong \angle H$, $\angle JIG \cong \angle HIF$, $\overline{GJ} \cong \overline{HK}$)

Answer:

$\triangle FGH \cong \triangle FKH$ by AAS congruence criterion.