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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.

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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

#### 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