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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

37

Concepts and
exercises

310+
  1. 1

    Introduction

    Explore the foundations of geometry without any rote memorization.

    1. Exploring Length

      Use your intuition and reasoning to find distances across and around shapes.

    2. Angle Hunt

      What's the missing angle?

    3. Working with Areas

      Manipulate shapes and apply your intuition and creativity to find areas.

  2. 2

    2D Geometry

    Find areas, perimeters, and more with common sense, not memorized formulas!

    1. Included with
      Brilliant Premium

      Angle Hunting

      Explore the relationships between angles that are in linear pairs, vertical pairs, and triangles.

    2. Included with
      Brilliant Premium

      Polygon Areas

      Find the areas of these polygons using your own reasoning rather than memorized formulas.

    3. Included with
      Brilliant Premium

      Circles

      Cut, rearrange, and strategize to solve these circle area problems.

    4. Included with
      Brilliant Premium

      Perimeters

      Explore the paths that pass through and around these polygons and circles.

  3. 3

    Going 3D

    Explore 3D shapes using logic and intuition rather than formulas.

    1. Included with
      Brilliant Premium

      Nets

      Fold up flat patterns to make 3D polyhedra.

    2. Included with
      Brilliant Premium

      Slicing Figures

      Dice, slice, and explore the cross-sections of 3D solids.

    3. Included with
      Brilliant Premium

      Surface Area

      Use your ingenuity to strategically solve for these surface areas.

    4. Included with
      Brilliant Premium

      Volume

      Pack the 3D volume of one solid shape with other, smaller solids!

  4. 4

    Pythagoras' Geometry

    Applying variables and algebraic techniques to the study of geometry.

    1. Included with
      Brilliant Premium

      Working Backward

      Start from the goal and work back to the beginning.

    2. Included with
      Brilliant Premium

      The Pythagorean Theorem

      Derive and use one of the most famous of all theorems.

    3. Included with
      Brilliant Premium

      Geometric Ratios

      Learn clever techniques for comparing areas and lengths.

    4. Included with
      Brilliant Premium

      Similarity

      In these challenges the same shape has been scaled to a variety of different sizes.

  5. 5

    The Coordinate Plane

    How geometry becomes algebra.

    1. Included with
      Brilliant Premium

      The Coordinate Plane

      Combine geometry with algebra!

    2. Included with
      Brilliant Premium

      Distance on a Graph

      Find how far it is between here and there.

    3. Included with
      Brilliant Premium

      Coordinate Geometry

      Apply coordinate strategies to geometric diagrams.

    4. Included with
      Brilliant Premium

      Rates of Change

      Plot movement over time.

  6. 6

    Intersections & Solutions

    Extending your uses for the coordinate plane.

    1. Included with
      Brilliant Premium

      Parallel Lines

      Explore the coordinate mathematics of lines that never meet.

    2. Included with
      Brilliant Premium

      Intersections

      Solve problems involving lines that cross.

    3. Included with
      Brilliant Premium

      Intersections Problem Solving

      Apply what you know about intersections to solve these challenging problems.

    4. Included with
      Brilliant Premium

      Perpendicular Lines

      How do you know when lines are at right angles to each other?

  7. 7

    When Geometry Gets Tough

    Apply what you’ve learned to these challenging problems.

    1. Included with
      Brilliant Premium

      When It Gets Tough

      Challenge yourself and use any strategies you want to solve these problems!

    2. Included with
      Brilliant Premium

      Challenging Composites

      Extend your best strategies even further and look for shortcuts.

    3. Included with
      Brilliant Premium

      Coordinate Geometry

      Return to the coordinate plane for some especially challenging coordinate puzzles.

    4. Included with
      Brilliant Premium

      Advanced Angle Hunting

      Go far beyond the first axioms and explore a realm where wild geometry flourishes.