The two column proof has shown that:
GC ≅ GB because Congruent parts of congruent triangles are congruent
How to prove Congruent Triangles?
There are different types of Congruency Postulates such as:
SAS Congruency Postulate
ASA Congruency Postulate
SSS Congruency Postulate
AAS Congruency Postulate
HL Congruency Postulate
The two column proof to show that GC and GB are congruent is:
Statement 1: A.F ≅ DE
Reason 1: Given
Statement 2: ∠A.FC ≅ ∠DEB
Reason 2: Given
Statement 3: ∠FAC ≅ EDB
Reason 3: Same base of congruent angles
Statement 4: ΔAFC ≅ ΔDEB
Reason 4: ASA Congruency Postulate
Statement 5: GC ≅ GB
Reason 5: Congruent parts of congruent triangles are congruent