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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

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

#### Angle Facts

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

2. Included with

#### Triangle Sides and Angles

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

3. Included with

#### Angle Hunting

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

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#### 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

#### Polygon Areas

How many squares do we need to build a triangle?

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#### Circles

How many triangles do we need to build a circle?

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#### Composite Figures

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

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#### 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

#### The Pythagorean Theorem

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

2. Included with

#### Applying the Pythagorean Theorem

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

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#### Coordinate Geometry

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

4. Included with

#### 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.

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#### Volume

How many cubes do we need to build a cylinder?

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#### Pyramids and Cones

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

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#### Geometric Ratios

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

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#### Similarity

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

6. 6

### When Geometry Gets Tough

Apply what you’ve learned to these challenging problems.

1. Included with

#### Finding Triangles

You'll need to use some triangular tricks to solve these problems.

2. Included with