Let us take by SSS these triangles are congruent.
So these two triangles have equal corresponding angles.
Consider the triangle GEC.
Recall that vertically opposite are always equal.
Hence triangles ABC and GEC have corresponding two angles that are equal.
If two corresponding angles are equal then third must be equal.
For example
By using the triangle sum property on triangle ABC, we get
Similarly to triangle GEC.
Comparing equations (1) and (2), we get that
Therefore triangles ABC and GEC are similar since their corresponding angles are congruent.