This Geometry course expands students’ knowledge of geometric concepts learned from previous courses. This course will expose students to a number of geometric topics aligned to the Common Core Standards.
In this course, students will focus on four critical areas:
Relate equations of geometric properties to writing and solving equations involving segments, angles, perimeter, and area.
Expand understanding of linear relationships to parallel and perpendicular lines.
Explore congruence and similarity and extend understanding to proving statements and theorems involving polygons and circles.
Synthesize and generalize properties of polygons to extend the learning of transformations and right triangle trigonometry.
Students will investigate topics such as geometric properties, congruence and similarity, and interpreting algebraic equations and inequalities geometrically. Translations of fixed objects on the coordinate plane as well as right triangle trigonometry will also be explored in detail. Students will also explore plane and solid geometric shapes with an emphasis on real world applications. Students will develop formal and informal proof using deductive reasoning skills. A variety of interactive tools and programs will be used to help students visualize and apply concepts.
This course incorporates a variety of textbook and multimedia resources including an adaptive problem set platform that provides various feedback on student assessments. In addition, students will use GeoGebra, an interactive tool that is used to investigate a variety of mathematical topics. This program will be used to analyze definitions, postulates, and theorems discussed throughout the course.
Students will engage in collaborative activities, such as simulations and discussions, and connect concepts in geometry to real-world applications, in order to develop a deeper understanding of geometry in the world.
In this standard-level course, students are expected to spend approximately 6 hours per week on their coursework.
Course Essential Questions:
- How do we apply geometric concepts and theorems to model situations?
- How are 2D objects and 3D objects related?
- How do we explain geometric relationships and formulas in problem solving?
- How do we define and apply trigonometric relationships to solve problems involving right triangles in the real world?
Course Learning Objectives:
- Interpret congruence and similarity in terms of rigid motions.
- Explain, prove, and apply geometric theorems.
- Make geometric constructions.
- Define trigonometric ratios.
- Explain geometric formulas and use them to solve problems.
- Visualize relationships between 2D and 3D objects.
- Apply geometric concepts in modeling situations.
- Apply trigonometric concepts to right triangles and to general triangles.