Using x, y, z values like lyounamu suggested:
Prove CF² + BE² = 3(x² + y²)
x = BA = AD = CD (sides of a square are equal)
y = DE = GF = GD (sides of a square are equal)
CG = z = y - x
x = y - z
y = z + x
Pythagoras' Theorem:
z² + y² = CF² ________(1)
x² + (x + y)² = BE²____(2)
x² + (2x + z)²...