1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$. 2. **Understand the given information:** We know both $a - b$ and $b - c$ equal 2. 3. **Calculate the numerator:** $$ (a - b)^2 + (b - c)^2 = 2^2 + 2^2 = 4 + 4 = 8 $$ 4. **Calculate the denominator:** First, find $a - c$: $$ a - c = (a - b) + (b - c) = 2 + 2 = 4 $$ Then square it: $$ (a - c)^2 = 4^2 = 16 $$ 5. **Form the fraction and simplify:** $$ \frac{(a - b)^2 + (b - c)^2}{(a - c)^2} = \frac{8}{16} = \frac{\cancel{8}}{\cancel{16}} = \frac{1}{2} $$ 6. **Final answer:** $$ \boxed{\frac{1}{2}} $$