# Geometry

We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
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## Angles and intersecting lines

This topic continues our journey through the world of Euclid by helping us understand angles and how they can relate to each other.

## Special properties and parts of triangles

You probably like triangles. You think they are useful. They show up a lot. What you'll see in this topic is that they are far more magical and mystical than you ever imagined!

## Transformations

In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations. You will learn how to perform the transformations, and how to map one figure into another using these transformations.

## Congruence

Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms.

## Similarity

Learn what it means for two figures to be similar, and how to determine whether two figures are similar or not. Use this concept to prove geometric theorems and solve some problems with polygons.

## Right triangles and trigonometry

Triangles are not always right (although they are never wrong), but when they are it opens up an exciting world of possibilities. Not only are right triangles cool in their own right (pun intended), they are the basis of very important ideas in analytic geometry (the distance between two points in space) and trigonometry.

## Circles

Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.

## Perimeter, area, and volume

A broad set of tutorials covering perimeter area and volume with and without algebra.

## Analytic geometry

In analytic geometry, also known as coordinate geometry, we think about geometric objects on the coordinate plane. For example, we can see that opposite sides of a parallelogram are parallel by by writing a linear equation for each side and seeing that the slopes are the same.

## Geometric constructions

We now have fancy computers to help us perfectly draw things, but have you ever wondered how people drew perfect circles or angle bisectors or perpendicular bisectors back in the day. Well this tutorial will have you doing just as your grandparents did (actually, a little different since you'll still be using a computer to draw circles and lines with a virtual compass and straightedge).

# Transformations

In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations. You will learn how to perform the transformations, and how to map one figure into another using these transformations.
Community Questions
All content in “Transformations”

## Introduction to rigid transformations

The three rigid transformations are translations, rotations, and reflections. Get to know them and gain some experience in performing them on different figures.

## Translations

Learn how to find the translation that maps a given figure to another, and how to manually draw the image of a translation.

## Rotations

Learn how to find the rotation that maps a given figure to another, and how to manually draw the image of a rotation.

## Reflections

Learn how to find the reflection that maps a given figure to another, and how to manually draw the image of a reflection.

## Dilations or scaling around a point

In addition to the three rigid transformation, there are the dilations, which expand or shrink figures while keeping the same proportions. These are extremely important in the subject of Similarity! Gain experience by performing dilation, learn how to find the dilation that maps a given figure to another, and learn how to manually draw the image of a dilation.

## Sequences of transformations

Learn how to analyze a sequence of different transformations performed in order.

## Properties and definitions of transformations

Let's continue our deep voyage through the world of transformations! Use your knowledge about the precise descriptions of the rigid transformations and their properties in various situations.

## Symmetry

Learn about different kinds of symmetries of two-dimensional shapes, and analyze various shapes according to their symmetries.