The ordering in assemblies of rigid-body rectangles is investigated statistical-mechanically, and the four kinds of liquid crystalline phases that appear as well as the transitions between some of the pairs of these phases are discussed. There appears one uniaxial nematic phase, two biaxial nematic phases, and one discotic phase. The phase diagram of the density versus the breadth-to-depth ratio of the rectangles is obtained; the four phases mentioned above appear in different regions depending on their molecular shape. Finally, the differences between the phase diagram of a system consisting of an assembly of rigid-body rectangles and that of a system of an assembly of biaxial molecules interacting via a dispersive force are discussed.