If you're seeing this message, it means we're having trouble loading external resources for Khan Academy.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Math

Geometry

This is a first year, high-school level course on Geometry (which is based on Euclid's elements). It revisits many of the basic geometrical concepts studied in earlier courses, but addresses them with more mathematical rigor. There is strong focus on proving theorems and results from basic postulates.
Community Questions
A thumbnail for: Introduction to Euclidean geometry
8 3

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.
A thumbnail for: Angles and intersecting lines
34 13

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.
A thumbnail for: Congruence
20 7

Congruence

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.
A thumbnail for: Similarity
14 7

Similarity

A thumbnail for: Right triangles and trigonometry
27 8

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.
A thumbnail for: Perimeter, area and volume
30 11

Perimeter, area and volume

A broad set of tutorials covering perimeter area and volume with and without algebra.
A thumbnail for: Circles
16 6

Circles

A thumbnail for: Special properties and parts of triangles
21 1

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!
A thumbnail for: Quadrilaterals
12 2

Quadrilaterals

A thumbnail for: Transformations
20 10

Transformations

Let's think more visually about things like shifts, rotations, scaling and symmetry.
A thumbnail for: Analytic geometry
8 5

Analytic geometry

A thumbnail for: Geometric constructions
8 4

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).
A thumbnail for: Worked examples
20 1

Worked examples

Sal does the 80 problems from the released questions from the California Standards Test for Geometry. Basic understanding of Algebra I necessary.
Congruence
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.

Transformations and congruence

Two figures are congruent if you can go from one to another through some combination of translations, reflections and rotations. In this tutorial, we'll really internalize this by working through the actual transformations.

Congruence postulates

We begin to seriously channel Euclid in this tutorial to really, really (no, really) prove things--in particular, that triangles are congruents. You'll appreciate (and love) what rigorous proofs are. It will sharpen your mind and make you a better friend, relative and citizen (and make you more popular in general). Don't have too much fun.