Absence of Triangles in Maximal Supergravity Amplitudes

16 pages, RevTeX4 formatFrom general arguments, we show that one-loop n-point amplitudes in colourless theories satisfy a new type of reduction formula. These lead to the existence of cancellations beyond supersymmetry. Using such reduction relations we prove the no-triangle hypothesis in maximal supergravity by showing that in four dimensions the n-point graviton amplitude contain only scalar box integral functions. We also discuss the reduction formulas in the context of gravity amplitudes with less and no supersymmetry