Free online courseGeometry

Course Description

Strengthen your math foundation by learning how to think like a geometer: define ideas precisely, reason logically, and prove results step by step. This course guides you from the very first building blocks of geometry to the tools that make complex problems manageable, helping you move beyond memorizing formulas and toward true understanding. You will practice reading diagrams correctly, translating visuals into statements, and recognizing which facts you can use in a proof without making hidden assumptions.

You will develop fluency with core geometric relationships, including angles created by lines and transversals, triangle and polygon properties, congruence and similarity, and the reasoning behind theorems you use in class. Along the way, you will build proof skills with a practical approach: learning how to plan, justify each step, and choose strategies such as direct reasoning, contrapositive thinking, and proof by contradiction. This makes geometry feel far less mysterious and much more like a structured problem-solving process you can repeat.

As you progress, you will connect geometry to measurement and the coordinate plane. You will work with circles, area and probability, and extend ideas into three-dimensional figures to understand surface area and volume. You will also see how algebra supports geometric thinking through proportions, trigonometric ratios in right triangles, slope and distance formulas, and coordinate proofs. Finally, transformations and symmetry tie many topics together, giving you a powerful way to interpret congruence, similarity, and patterns in the plane and in space. By the end, you will be better prepared for school assessments and for any next-step course that depends on rigorous reasoning.