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Geometry Fundamentals

An intuitive introduction to the essentials of geometry.

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.

Interactive
quizzes

24

Concepts and
exercises

255+
  1. 1

    Introduction

    Cuts, folds, and rearrangements — see how hands-on manipulation of shapes can reveal the truth without a calculation.

    1. Calculating Area

      Geometry is a way of thinking — sometimes a new perspective can save a calculation.

    2. Cutting Shapes

      Slice and dice to make reasoning about shapes more intuitive.

    3. Angles in Polygons

      Reason your way from basic angle properties to a universal truth of triangles.

  2. 2

    Angles and Lengths

    Angle and length — geometry's basic units of measure — are tools in the detective hunt to characterize new shapes.

    1. Included with
      Brilliant Premium

      Angle Facts

      Build up a toolbox of angle ideas to discover geometric principles.

    2. Included with
      Brilliant Premium

      Triangle Sides and Angles

      Sides and angles — the unbreakable partnership that makes triangles what they are today.

    3. Included with
      Brilliant Premium

      Angle Hunting

      Put your knowledge of angles to work to track down the missing information in these shape puzzles.

    4. Included with
      Brilliant Premium

      Perimeters

      Trace the borders of your understanding by exploring the paths around shapes.

  3. 3

    Area

    From the circle to the pyramid, the area of many shapes can be found by building them out of rectangles.

    1. Included with
      Brilliant Premium

      Polygon Areas

      How many squares do we need to build a triangle?

    2. Included with
      Brilliant Premium

      Circles

      How many triangles do we need to build a circle?

    3. Included with
      Brilliant Premium

      Composite Figures

      To conquer new shapes, it helps to catch a glimpse of the old.

    4. Included with
      Brilliant Premium

      Surface Area

      How much paint do we need to redecorate a prism?

  4. 4

    Pythagoras' Geometry

    Discover the famous law of right triangles using the power of perspective, and learn how to apply it in several different contexts.

    1. Included with
      Brilliant Premium

      The Pythagorean Theorem

      Unlock Pythagoras’ famous formula by looking at the same triangle in two different ways.

    2. Included with
      Brilliant Premium

      Applying the Pythagorean Theorem

      If at first you can't see a triangle in your problem, you might not be looking hard enough.

    3. Included with
      Brilliant Premium

      Coordinate Geometry

      Overlay a grid and any problem can be a geometry problem.

    4. Included with
      Brilliant Premium

      Coordinate Distance

      With a grid and Pythagoras, we can find any distance.

  5. 5

    Scaling and Volume

    With area as a base, use symmetry and slice to find the volume of shapes.

    1. Included with
      Brilliant Premium

      Volume

      How many cubes do we need to build a cylinder?

    2. Included with
      Brilliant Premium

      Pyramids and Cones

      Through symmetry and slice, discover the volume of these solids without an ounce of calculus.

    3. Included with
      Brilliant Premium

      Geometric Ratios

      How do the pieces of a shape relate to one another?

    4. Included with
      Brilliant Premium

      Similarity

      Can we use our knowledge of one shape to find the measurements of another?