Geometry Syllabus

Geometry is an engaging, interactive course designed for students who have completed Algebra A or an equivalent introductory algebra course. Aligned with the Common Core State Standards for Geometry, this course guides students through essential Euclidean constructions, from simple polygons and circles to complex polyhedra and 3-D surfaces. Students will develop skills in logical proofs, analytical geometry, and trigonometry, while deepening their understanding of key concepts like the Pythagorean theorem and radical simplification. Incorporating problem-solving exercises, logic puzzles, and competition-style challenges, Geometry keeps young minds active and inspired as they explore the exciting relationships and structures within mathematics.

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Required Textbook: Art of Problem Solving: Geometry

Required for: Pre-Calculus

Concepts, skills, and learning tools students see in this course include, but are not limited to:

• Geometric Constructions and Definitions: Explore foundational Euclidean constructions and definitions.
• Triangles and Their Properties: Study triangle congruence, similarity, right triangles, and key triangle centers (medians, altitudes, etc.).
• Polygons and Inequalities: Understand properties of quadrilaterals, polygons, and geometric inequalities.
• Circles and Trigonometry: Examine circles, angles, and introductory trigonometric functions.
• Problem-solving skills, logic puzzles, algebraic and geometric thinking, competition-style problems

Upon completing the course, students will be able to:

• Geometric Constructions and Logic: Build specific geometric objects from foundational principles, enhancing logical reasoning skills.
• Triangle Similarity and Congruence: Apply principles of similarity and congruence to solve problems involving triangles.
• Circle Theorems and Applications: Understand and use theorems involving chords, tangents, sectors, and segments within circles.
• 3D Visualization and Trigonometry: Visualize relationships between 2D and 3D objects, solve geometric equations, and use basic trigonometric functions to find missing values in right triangles.

Students registering for this course should be comfortable with the following Math:‍

• Arithmetic with Rational and Radical Numbers: Master operations with all types of rational and radical numbers.
• Graphing on the Cartesian Plane: Accurately draw and label points on a Cartesian plane.
• Translating Word Problems: Convert word problems into mathematical expressions or visual representations.
• Using Variables in Algebraic Expressions: Confidently incorporate variables in expressions and equations.
• Completion of Algebra A (or Algebra 1) or equivalent

• Foundations and Constructions (8 weeks): Learn the basics of Euclidean geometry, including points, lines, angles, and foundational constructions like bisectors and triangles, while exploring types of proofs and essential geometric tools.
• Triangles, Polygons, and Circle Theorems (9 weeks): Study triangle properties, congruence, similarity, and theorems involving polygons and circles. Understand key principles such as the Pythagorean theorem, trigonometric functions, and circle theorems like inscribed angles and tangents.
• Advanced Triangle and Quadrilateral Properties (7 weeks): Examine triangle centers (medians, altitudes), quadrilaterals, and geometric inequalities, applying these properties to solve complex geometric problems.
• 3D and Curved Geometry (8 weeks): Explore the properties and measurements of 3D shapes like prisms, pyramids, and polyhedra, as well as curved figures such as cylinders, cones, and spheres, covering surface area and volume calculations.
• Transformations and Analytic Geometry (6 weeks): Learn transformations (translations, rotations, reflections, dilations) and apply analytic geometry on the Cartesian plane to solve equations of lines, circles, and advanced problems in distance and proof.