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# Geometry I

## Build a foundation for geometry with angles, triangles, and polygons.

In this course, you'll solve delightful geometry puzzles and build a solid foundation of skills for problem-solving with angles, triangles, and polygons. You'll also improve your visual intuition and learn how to come up with clever, creative solutions to tough challenges.

This course is the perfect place to start (or continue) your exploration of geometry if you know how to measure angles and calculate the areas of rectangles, circles, and triangles; and want to learn the next level of geometric problem-solving techniques.

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1. 1

### Introduction

Get started with 2D on a journey with polygons and clever geometry puzzles.

1. #### Triangles and Hexagons

Get started by thinking about patterns that combine triangles and hexagons.

2. #### Strategic Geometry

Work out strategies to approach these area challenges.

3. #### Driving on a Polygon

Derive a fundamental theorem of geometry!

2. 2

### Angles

Beware: even a cute little angle can bite!

1. Included with
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#### Angle Hunting Axioms

Practice finding missing angles.

2. Included with
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#### Advanced Mental Shortcuts

Learn sneaky strategies for solving tough angle problems.

3. Included with
Brilliant Premium

#### Internal Angles in a Polygon

Solve angle problems involving polygons that have many sides.

4. Included with
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#### Invariant Angle Sets

Investigate scenarios where the sum of several angles stays constant.

3. 3

### Triangles

Endless complexity can come from just three sides.

1. Included with
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#### The Triangle Inequality

In what circumstances can you make a triangle?

2. Included with
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#### Congruent and Similar Triangles

When are triangles the same?

3. Included with
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#### Bass Fishing

Investigate a special case where a triangle can be drawn two ways.

4. Included with
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#### Curry's Paradox

Uh... Where did the missing square go?

4. 4

### Composite Polygons

Celebrate the surprising truths inherent to the mathematics of space.

1. Included with
Brilliant Premium

#### Warm-ups

Warm up your problem-solving muscles by exploring these shape-combining diagrams.

2. Included with
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#### Adding Lines and Grids

Add lines to help clarify your thinking.

3. Included with
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#### Complementary Areas

Sometimes it's easier to find the area of what's left after your shape is removed...

4. Included with
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#### Inclusion and Exclusion

What happens when shapes overlap?

5. 5

### Regular Polygons

From perimeters and pi to stellations and tessellations.

1. Included with
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#### Angles of Regular Polygons

When all of the sides are the same length and all of the angles are the same measure, what else must be true?

2. Included with
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#### Is It Regular?

Can you be absolutely certain that each of these polygons is regular?

3. Included with
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#### Polygon Areas and Lengths

Apply the Pythagorean Theorem to find length and area measures of regular polygons.

4. Included with
Brilliant Premium

#### Matchstick Polygons

Play around with these polygons made out of matchsticks, q-tips, and toothpicks.