To prove two triangles are similar, we only need two pairs of congruent angles.
The first pair of congruent angles could be the two right angles AED and GFC as shown by the square markers.
As for the other pair of congruent angles, we could pick on angle DAE and angle FGC, which are corresponding angles. The corresponding angles are congruent because of the vertical parallel line segments BA and FG
Once you have two pairs of congruent angles, you have effectively wrapped up the similarity proof. The specific theorem you use is the AA (angle angle) similarity theorem.
