The high school standards are listed in conceptual categories. Geometry is one of the 5 conceptual categories. During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions and developing careful proofs. Later in college some students develop Euclidean and other geometries carefully from a small set of axioms. Dynamic geometry environments provide students with experimental and modeling tools that allow them to investigate geometric phenomena in much the same way as computer algebra systems allow them to experiment with algebraic phenomena.
Key Contents: Congruence (CO) • Experiment with transformations in the plane • Understand congruence in terms of rigid motions • Prove geometric theorems • Make geometric constructions Similarity, Right Triangles, and Trigonometry (SRT) • Understand similarity in terms of similarity transformations • Prove theorems involving similarity • Define trigonometric ratios and solve problems involving right triangles • Apply trigonometry to general triangles Circles (C) • Understand and apply theorems about circles • Find arc lengths and areas of sectors of circles Expressing Geometric Properties with Equations (GPE) • Translate between the geometric description and the equation for a conic section • Use coordinates to prove simple geometric theorems algebraically Geometric Measurement and Dimension (GMD) • Explain volume formulas and use them to solve problems • Visualize relationships between two-dimensional and three-dimensional objects Modeling with Geometry (MG) • Apply geometric concepts in modeling situations