Students are familiar with some geometric properties from previous mathematics classes but now have the tools to prove them true. The study is extended to other polygons and circles as well as 3-D figures. In the spirit of classical geometry, students create constructions and discuss why the constructions work. Students also derive, verify, and apply formulas for angle measure, length, area, and volume of regular and irregular figures. Similarity and Congruence Relationships between geometric figures are a major theme of the geometry course.
Students study methods of proving the similarity or congruence of triangles and other polygons.
This topic is particularly rich in applications, giving students opportunities to apply their knowledge of similarity and congruence to solve word problems and determine heights, lengths, areas, and angles. Trigonometry is a natural outgrowth of the study of similar triangles where students learn the definitions of the trigonometric ratios, find values for special angles, and engage in problem-solving applications. While studying affine geometry, students apply properties of mappings and relations to prove theorems about points, lines, and planes. The ability to solve equations and determine terms in a proportion is crucial for solving problems in the similarity unit. While studying coordinate geometry, students apply their knowledge of graphing to prove theorems about geometric figures.