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Khan Academy is a 501(c)(3) nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. Our interactive practice problems, articles, and videos help students succeed in math, biology, chemistry, physics, history, economics, finance, grammar, and many other topics.

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Watch the 1st video of the course

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We don't normally delve too far into history when talking about math, but sometimes it's important to have perspective about how some of our math concepts came about and how influential they have become.

Watch the next lesson: https://www.khanacademy.org/math/geometry/intro_euclid/v/language-and-notation-of-basic-geometry?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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, ci

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Before learning any new concept (mathematical or otherwise), it's important we learn and use a common language and label concepts consistently.

Watch the next lesson: https://www.khanacademy.org/math/geometry/intro_euclid/v/lines-line-segments-and-rays?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/intro_euclid/v/euclid-as-the-father-of-geometry?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 specifi

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Let's get familiar with the difference between lines, line segments, and rays. Hint: a ray is somewhere between a line and a line segment!

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/intro_euclid/e/recognizing_rays_lines_and_line_segments?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/intro_euclid/v/drawing-lines-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/intro_euclid/v/language-and-notation-of-basic-geometry?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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

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Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs

Watch the next lesson: https://www.khanacademy.org/math/geometry/intro_euclid/v/the-golden-ratio?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/intro_euclid/v/geometric-precision-practice?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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, righ

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The naming of an angle is related to the line segments that create it. We'll also learn about the angle's vertex. Come on. Let's do this.

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/measuring-angles-in-degrees?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/intro_euclid/v/identifying-ray?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 th

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Let's come up with an exact way to measure an angle using a protractor. We'll also learn about acute angles. Not to be confused with augly angles :)

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/using-a-protractor?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/angle-basics?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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.

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Let's use our virtual protractor to measure some angles together, shall we?

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/measuring-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/measuring-angles-in-degrees?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 cove

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We're practicing measuring angles using the virtual protractor. Do this a few times with us and you'll use a real protractor like a pro!

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/e/measuring_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/acute-right-and-obtuse-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/using-a-protractor?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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-

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Let's add some tools to our geometry tool belt. Here's a thorough explanation of complementary and supplementary angles, as well as definitions of adjacent and straight angles.

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/complementary-supplementary-angl/e/complementary_and_supplementary_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/complementary-supplementary-angl/v/example-using-algebra-to-find-measure-of-complementary-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/old_angles/v/acute-right-and-obtuse-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things

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By using our knowledge of supplementary, adjacent, and vertical angles, we can solve problems involving the intersection of two lines, including this one!

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/e/vertical_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/using-algebra-to-find-the-measures-of-vertical-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/angle-measurement-and-circle-arcs?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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

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Proving that vertical angles are equal

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/e/congruent_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/angles-formed-by-parallel-lines-and-transversals?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/using-algebra-to-find-the-measures-of-vertical-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 (a

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Parallel lines, transversal lines, corresponding angles

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/e/congruent_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/identifying-parallel-and-perpendicular-lines?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/proof-vertical-angles-are-equal?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 everyt

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Proof that the sum of the measures of the angles in a triangle are 180

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Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof-sum-of-measures-of-angles-in-a-triangle-are-180?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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--i

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Another example finding angles in triangles

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-3?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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, int

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Multiple ways to solve for the angles of multiple triangles

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/challenging-triangle-angle-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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

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Interesting problem finding the sums of particular exterior angles of an irregular pentagon

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof-corresponding-angle-equivalence-implies-parallel-lines?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-3?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 yo

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Proof by contradiction that corresponding angle equivalence implies parallel lines

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/finding-more-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/challenging-triangle-angle-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 spe

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Example of angle hunting!

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/e/angles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/sum-of-interior-angles-of-a-polygon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof-corresponding-angle-equivalence-implies-parallel-lines?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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 everyt

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Showing a generalized way to find the sum of the interior angles of any polygon

Practice this lesson yourself on KhanAcademy.org right now:

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/e/angles_of_a_polygon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/sum-of-the-exterior-angles-of-convex-polygon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/finding-more-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: 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

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