Understands and applies properties and relationships of geometric figures
Geometric objects, such as triangles, have many important and useful properties and relationships. For example, a triangle might have the property of being a right triangle (having one angle that measures 90 degrees), or two triangles might have the relationship of being congruent (having the same size and shape).
Students should be able to visualize, describe, reason about, and apply properties and relationships of two- and three-dimensional objects. Specific geometric skills students should demonstrate include visualizing, drawing, geometric modeling, making and testing conjectures, and using inductive and deductive reasoning.
The primary focus should be on two-dimensional objects, their properties and relationships. Particular emphasis should be given to properties of angles, lines, polygons, and circles. In three dimensions, students should be able to visualize, draw, and compute measurements of simple three-dimensional shapes.
Measurement skills and concepts should be included in the study of geometry including finding perimeter, area, volume and surface area. Estimation, appropriate units, dimensional analysis, and judgments about accuracy should be part of the study of measurement.
Properties and relationships of geometric objects should be examined and justified, including similarity, congruence, and measurement. Objects should be represented with drawings, coordinates, and matrices, and transformations of the objects should be investigated.