Sharp faceted interfaces are often observed between compound precipitates and matrix phases, which are remarkably different in their lattice parameters. Multiple orientation relationships (ORs) corresponding to various faceted interfaces tend to coexist in one alloy. A near row matching (NRM) approach is proposed for a systematic investigation of ORs corresponding to potential preferred interfaces. Unlike a common practice to search for misorientations corresponding to low sigma grain boundaries associated with matching periodicity in three dimensions (3D), this approach directly searches for ORs that permit local 2D periodic good matching structures in preferred interfaces. The calculation method consists of two simple steps to evaluate matching within and between rows of lattice points. The method has been applied to a Mg2Sn/Mg system. Ten of the forty-four predicted facets agree with the experimental observations, for the cases that the preferred facets can be described (approximately) by low index planes of the precipitates. The predictions can cover all known observations, if limited high index planes are included as candidates. Each observed facet is characterized with a periodic pattern of good matching sites (GMSs) in localized regions. NRM is a necessary condition for the existence of a periodic GMS pattern. The agreement between the calculation results and experimental results confirms the important role of periodic matching in the development of preferred interfaces and their corresponding ORs. It also demonstrates the usefulness of geometric matching study for quantitative predictions of potential preferred interfaces.