Geometry
Geometry is the study of shape. We can begin by considering, in a sense, the situation of no shape. That is, consider geometric diagrams consisting of vertices and edges in which shape is not essential, only the connections among vertices are essential. Such diagrams are called vertex-edge graphs. These graphs are widely used in business and industry to study problems about paths (e.g., finding a shortest path or a critical path), networks (e.g., optimizing a telecommunications network), and relationships among a finite number of elements (e.g., avoiding conflicts when scheduling committee meetings for people who are members of more than one committee). Continuing the study of shape, consider properties of and relationships among shapes (including two- and three-dimensional shapes), location of shapes (leading to coordinate geometry), transformations of shapes (leading to transformation geometry), special shapes (such as circles and triangles, leading to trigonometry), and reasoning about shape (including geometric proof). All these aspects of shape are captured in the geometry essential topics listed and described below.
Technology should be used appropriately throughout the teaching and learning of geometry. This may include the use of graphing calculators, interactive geometry software, and resources on the Internet. Such technology should be used, for example, to facilitate an experimentation and conjecturing approach to teaching and learning geometry.
Essential Topics in Geometry:
- Understands and applies coordinates | Details | Example
- Understands and applies transformations | Details | Example
- Understands and applies properties and relationships of geometric figures | Details | Example
- Understands and applies trigonometric relationships | Details | Example
- Understands and applies vertex-edge graphs | Details | Example