This monograph provides an epistemological rational to aid educators with the design of inquiry in trichotomous research. “Triangular Equation Modeling” (or “TEM”) is a simple but precise research methodology for the creation of accurate and in–depth research questions, and trichotomous variables for the aggregation of data on a specifically identified criterion. Triangular Equation Modeling builds the foundation for the Tri-Squared Test in a Tri-Coordinate set of variables in dual Cartesian coordinates [x and y]. It is a basic research method that involves detailing research principles in a precise isometric model so that instrumentation can be created for research analysis and investigation.