The main facets of geometry, according to the National Council of Teachers of Mathematics, are to "analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; specify locations and describe spatial relationships using coordinate geometry and other representational systems; apply transformations and use symmetry to analyze mathematical situations; [and] use visualization, spatial reasoning, and geometric modeling to solve problems." For measurement, students should "understand measurable attributes of objects and the units, systems, and processes of measurement; [and] apply appropriate techniques, tools, and formulas to determine measurements" (NCTM, 2000, pp. 41-44).