Moving towards formal mathematical arguments, the standards presented in this high school geometry course are meant to formalize and extend middle grades geometric experiences. Transformations are presented early in the year to assist with the building of conceptual understandings of the geometric concepts.
In unit 1, triangle congruence conditions are established using analysis of rigid motion and formal constructions. Various formats will be used to prove theorems about angles, lines, triangles and other polygons. The work in unit 2 will build on the students understanding of dilations and proportional reasoning to develop a formal understanding of similarity.
The standards included in unit 3 extend the notion of similarity to right triangles and the understanding of right triangle trigonometry. In developing the Laws of Sines and Cosines, the students are expected to find missing measures of triangles in general, not just right triangles.
Work in unit 4 will focus on circles and using the rectangular coordinate system to verify geometric properties and to solve geometric problems. Concepts of similarity will be used to establish the relationship among segments on chords, secants and tangents as well as to prove basic theorems about circles.
The standards in unit 5 will extend previous understandings of two- dimensional objects in order to explain, visualize, and apply geometric concepts to three-dimensional objects. Informal explanations of circumference, area and volume formulas will be analyzed.
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