Additional information required in order to know that ∆ACB ≅ ∆BGA are congruent for the given reason AAS Postulate is : the prove that angleCAB ≅ angleGBA
How to prove the congruence of triangles.
To prove triangles congruent using the AAS postulate, we need information about two angles and a non-included side in both triangles.
The "non-included side" in a triangle refers to the side that is not between the two specified angles when using an angle-side-angle (ASA) or angle-angle-side (AAS) congruence criterion.
From the figure
Given
angleACB ≅ angleBGA(Given)
AB ≅ AB (Reflective property of ≅)
Then,
angleCAB ≅ angleGBA (alternate postulate, CA||GB).
∆ACB ≅ ∆BGA (Angle-Angle-Side)
This will complete the prove of the congruence of the triangles by the reason AAS postulate.