Given ABDE and AFGC are squares and ABC is a right triangle.
To prove: triangle EAC congruent to triangle BAF
Proof:
Consider triangles EAC and BAF:
1) EA = AB [EA and AB are sides of the square ABDE]
2) AC = AF [AC and AF are sides of the square AFGC]
3) ∠EAC=∠EAB+∠BAC∠BAF=∠BAC+∠CAF[∠EAB=∠CAF=90deg]⟹∠EAC=∠BAF
Hence the triangles EAC and BAF are congruent by SAS rule.