Geometry

Credits: 1

Course Length

2 Semesters

Based on plane Euclidean geometry, this rigorous full-year course addresses the critical areas of: congruence, proof, and constructions; similarity and trigonometry; circles; three-dimensional figures; and probability of compound events. Transformations and deductive reasoning are common threads throughout the course. Students build on their conceptual understanding of rigid transformations established in middle school as they formally define each and then, use them to prove theorems about lines, angles, and triangle congruency. Rigid transformations are also used to establish relationships between two-dimensional and three-dimensional figures.

Students use their knowledge of proportional reasoning and dilations to develop a formal definition for similarity of figures. They apply their understanding of similarity to defining trigonometric ratios and radian measure. Students also make algebraic connections as they use coordinate algebra to verify properties of figures in the coordinate plane and write equations of parabolas and circles. Throughout the course, students investigate properties of figures, make conjectures, and prove theorems. Students demonstrate their reasoning by completing proofs in a variety of formats. The standards of mathematical practice are embedded throughout the course as students apply geometric concepts in modeling situations, make sense of problem situations, solve novel problems, reason abstractly, and think critically.

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Overview of Concepts

• Unit 1: Foundations of Euclidean Geometry
• Unit 2: Geometric Transformations
• Unit 3: Angles and Lines
• Unit 4: Triangles
• Unit 5: Triangle Congruence
• Unit 6: Similarity Transformations
• Unit 7: Right Triangle Relationships and Trigonometry
• Unit 8: Quadrilaterals and Coordinate Algebra
• Unit 9: Circles
• Unit 10: Geometric Modeling in Two Dimensions
• Unit 11: Geometric Modeling in Three Dimensions
• Unit 12: Applications of Probability