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.
Contents
The Best of Geometry on Brilliant
Within geometry, you can learn about wide-ranging topics such as the following:
Geometry Topic Area Map
| \(\hspace{35mm}\) | Wiki Page Index | Practice Quizzes\(\hspace{20mm}\) | \(\hspace{35mm}\) | Wiki Page Index | Practice Quizzes |
| Geometric Measurement |
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| Triangles |
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| Polygons |
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| Circles |
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| Coordinate Geometry |
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| Trigonometry |
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| Trigonometric Identities |
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| Vectors |
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| 3D-Geometry |
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| Euclidean Geometry |
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| Geometric Transformations |
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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:
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.
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