Geometry Overview

The topography of a mountain range, the maximum tilt of a space shuttle before launch, and the path of a pool ball when it bounces off the side are all measured and understood using the fundamental tools of geometry: lines, angles, shapes, and coordinate maps. Whether you're looking for practice problems for school math and Olympiad competition topics, or for advanced, open-ended challenges, we have something here for you. The collection of Brilliant problems and articles is large and growing.

The Best of Geometry on Brilliant

Within geometry, you can learn about wide-ranging topics such as the following:

Pythagorean Theorem

Parabolas: Focus and Diretrix

Composite Figures

Alternate Segment Theorem

Möbius Strips

Common Misconceptions

Geometry Topic Area Map

$\hspace{35mm}$	Wiki Page Index	Practice Quizzes $\hspace{20mm}$	$\hspace{35mm}$	Wiki Page Index	Practice Quizzes
	Geometric Measurement			Triangles
	Polygons			Circles
	Coordinate Geometry			Trigonometry
	Trigonometric Identities			Vectors
	3D-Geometry			Euclidean Geometry
	Geometric Transformations

Common Geometry Notations

The following notations are commonly used in geometry:

Notation	Definition
$\angle$	angle
$\triangle$	triangle
$\|F\|$	Area of figure $F$
$\parallel$	parallel
$\perp$	perpendicular to
$\sim$	similar to (commonly used for similar figures)
$\equiv$	congruent to (commonly used for congruent figures)
$\in$	belongs to the set/belongs to the line (for points)
$\cap$	intersection (for sets and lines )
$\subset$	subset of
$\stackrel\frown{AB}$	arc $AB$
$\overleftrightarrow{AB}$	line $AB$
$[AB]$	line segment $AB$
$[AB)$	ray $AB$ or line segment $AB$ excluding $B$
$\overrightarrow{AB}$	vector $AB$ or the directed length $AB$

Curriculum Geometry Content

Brilliant's article collection is expanding to cover every topic you might encounter in any pre-collegiate math program. In most topic areas, we cover the content in much more depth than traditional grade-school standards, with a focus on real understanding instead of memorization.

The most popular pre-collegiate geometry topics on Brilliant are as follows:

Triangle Area Formulas

Pythagorean Theorem

Regular Polygons

Trigonometric Equations

Symmetry

Graph Transformation

Extracurricular Geometry Content

Our goal is to be able to challenge any student in the world with math that stretches their skills. The topics below are at the collegiate level or beyond, including some math topics that you likely wouldn't see in school unless you majored in math at a top tier college.

Angle Bisector Theorem

Pitot's Theorem

Möbius Strips

Fractals

And that's only the tip of the iceberg. There's much more advanced geometry on Brilliant, and if you don't see a page that you think we should have, please contribute it.

Competitions, Exams and Olympiads

Whether you're just beginning to study for your first math competition, or if you're a pro aiming for a perfect score, Brilliant is a resource for every trick and topic that you might be looking for. The competitions and exams that Brilliant can help you study for include the following:

International Math Competitions

IMO
IMC
Mathematical Kangaroo

USA Math Exams and Competitions

AIME
AMC8 / AMC10 / AMC12
AP Exams (AB Calculus, BC Calculus)
ARML
MATHCOUNTS
MOEMS
SAT
USAMO
USAJMO
USAMTS

Indian Math Exams and Competitions

RMO
KVPY
IIT JEE

Contents