In the given picture , we have two triangles ΔHIG and Δ FIE , in which
[given]
[given]
Also, [Vertically opposite angles]
Therefore by SAS congruence postulate we have
SAS congruence postulate says that if two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle then we say that the two triangles are congruent.