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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Introduction to Euclidean geometry

Roughly 2400 years ago, Euclid of Alexandria wrote Elements which served as the world's geometry textbook until recently. Studied by Abraham Lincoln in order to sharpen his mind and truly appreciate mathematical deduction, it is still the basis of what we consider a first year course in geometry. This tutorial gives a bit of this background and then lays the conceptual foundation of points, lines, circles and planes that we will use as we journey through the world of Euclid.

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.


It's time to learn about the most useful math concept for creating video game graphics: geometric transformations.


If you can take one figure and flip, shift, and rotate (not resize) it to be identical to another figure, then the two figures are congruent. This topic explores this foundational idea in geometry.


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.

Perimeter, area, and volume

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


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!


Analytic geometry

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).

Worked examples

Sal does the 80 problems from the released questions from the California Standards Test for Geometry. Basic understanding of Algebra I necessary.
All content in “Circles”

Central, inscribed and circumscribed angles

We'll now dig a bit deeper in our understanding of circles by looking at central, inscribed and circumscribed angles. This is fun and beautiful as is, but you'll also see that it shows up on a lot of math standardized tests. Why do people like to put geometry like this on standardized tests? Because it shows deductive reasoning skills which are super important in every walk of life!

Area of inscribed triangle

This more advanced (and very optional) tutorial is fun to look at for enrichment. It builds to figuring out the formula for the area of a triangle inscribed in a circle!