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We compare the relative strength of valid inequalities for the integer hull of the feasible region of mixed integer linear programs with two equality constraints, two unrestricted integer variables and any number of nonnegative continuous variables. In particular, we prove that the closure of Type 2 triangle (resp. Type 3 triangle; quadrilateral) inequalities, are all within a factor of $$1.5$$ 1.5 of the integer hull, and provide examples showing that the approximation factor is not less than $$1.125$$ 1.125 . There is no fixed approximation ratio for split or Type 1 triangle inequalities however.

On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs