  Integer programs defined by two equations with two free integer variables and
nonnegative continuous variables have three types of nontrivial facets: split,
triangle or quadrilateral inequalities. In this paper, we compare the strength
of these three families of inequalities. In particular we study how well each
family approximates the integer hull. We show that, in a well defined sense,
triangle inequalities provide a good approximation of the integer hull. The
same statement holds for quadrilateral inequalities. On the other hand, the
approximation produced by split inequalities may be arbitrarily bad.
