The SAS or the side-angle-side theorem states that two triangles are equal if two sides and the angle between them are equal. As you can see in your figure:
Between ΔIGH and ΔFDE
m∠ IGH ≅ m∠FDE
side IG ≅ side FD
side GH ≅ side DF
So based on that SAS postulate proves that the triangles are congruent.
