In a fixed-effects model, suppose that there are n observations for each of four treatments. Let Q²₁ Q²₂, and Q²₃ be single-degree-of-freedom sums of squares for orthogonal contrasts. A contrast is a linear combination of the treatment means with coefficients that sum to zero. The coefficient vectors of orthogonal contrasts are orthogonal vectors. Prove that SS_Treatments = Q²₁ +Q²₂ + Q²₃.