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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
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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.
A thumbnail for: Angles and intersecting lines
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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.
A thumbnail for: Congruence
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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
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Similarity

A thumbnail for: Right triangles and trigonometry
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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
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Perimeter, area and volume

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

A thumbnail for: Special properties and parts of triangles
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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
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Quadrilaterals

A thumbnail for: Transformations
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Transformations

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

A thumbnail for: Geometric constructions
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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
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Worked examples

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

Equation of a circle

You know that a circle can be viewed as the set of all points that whose distance from the center is equal to the radius. In this tutorial, we use this information and the Pythagorean Theorem to derive the equation of a circle.

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!

Geometric models

Let's use what we know about geometry to answer some really, really interesting questions.