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.

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1. 1

Introduction

Explore the foundations of geometry without any rote memorization.

1. Exploring Area

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

2. Going 3D

Sample some of the peculiarities of the third dimension with these geometric riddles.

3. Angle Hunt

What's the missing angle?

2. 2

2D Geometry

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

1. Included with

Angle Hunting

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

2. Included with

Polygon Areas

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

3. Included with

Circles

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

4. Included with

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

Nets

Fold up flat patterns to make 3D polyhedra.

2. Included with

Slicing Figures

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

3. Included with

Surface Area

Use your ingenuity to strategically solve for these surface areas.

4. Included with

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

Working Backward

Start from the goal and work back to the beginning.

2. Included with

The Pythagorean Theorem

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

3. Included with

Geometric Ratios

Learn clever techniques for comparing areas and lengths.

4. Included with

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

The Coordinate Plane

Combine geometry with algebra!

2. Included with

Distance on a Graph

Find how far it is between here and there.

3. Included with

Coordinate Geometry

Apply coordinate strategies to geometric diagrams.

4. Included with

Rates of Change

Plot movement over time.

6. 6

Intersections & Solutions

Extending your uses for the coordinate plane.

1. Included with

Parallel Lines

Explore the coordinate mathematics of lines that never meet.

2. Included with

Intersections

Solve problems involving lines that cross.

3. Included with

Intersections Problem Solving

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

4. Included with

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

When It Gets Tough

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

2. Included with

Challenging Composites

Extend your best strategies even further and look for shortcuts.

3. Included with