Foundational Math · Level 3


Start exploring geometry with an intuitive introduction to the essentials.

Angles in Polygons

Exterior and Interior Angles

Polygon Angle Relationships

Angles Made by Lines

Parallel Lines

Triangle Sides and Angles



Arc Length

Scaling Shapes

Scaling Lengths

Reasoning About Area

Polygon Areas

Circle Areas

Scaling Areas

The Pythagorean Theorem

Using the Pythagorean Theorem

Squares and Roots

Special Right Triangles


Surface Area

Surface Area Shortcut

Pyramids and Cones


Pyramids and Cones

Course description

Discover how intuitive geometry can be when you keep your assumptions simple and use your own logic and reasoning to set up your calculations. This fundamentals course will introduce you to angle axioms, perimeter and area calculation strategies, coordinate geometry, 3D geometry, and more. This is the course that you should begin with if you're just starting your exploration of geometry on Brilliant. Some prior experience with algebra is assumed, but you're in good shape to start this course if you can plot points and linear equations on a coordinate plane and use a variable to describe the relationship between the side length of a square and its area. And, by the end of this course, you’ll be a skilled geometric problem-solver, well practiced at everything from proving the Pythagorean theorem to mixing algebraic and geometric techniques together on the coordinate plane.

Topics covered

  • Angle Axioms
  • Measuring Areas
  • Parallel and Perpendicular Lines
  • Perimeter
  • Similarity
  • Surface Area
  • The Pythagorean Theorem
  • Three-Dimensional Figures
  • Volume

Prerequisites and next steps

You should have a basic understanding of algebra concepts covered in Solving Equations.


  • Solving Equations

Up next

Foundational Math · Level 4


Use vectors — a way of describing a move in space — to program a game and design a logo.

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