Why is a triangle 180° ?

This is a visualization of the proof that a triangle's angles sum to 180 degrees.

Technical note: the key assumption is there is exactly 1 parallel to the right side passing through the left point. This is the parallel postulate of plane geometry (the standard one we learn in grade school). There are other types of geometries where triangle angles sum to more or less than 180 degrees (in hyperbolic geometry, there would similarly be infinitely many such lines, and a triangle's angles sum to less than 180 degrees. This is the geometry of special relativity).

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[ak_the_gr]

Everybody gangsta until he started shaking the triangle

[rrodriguez]

Loved your choice of music . No words needed for an explanation. Understood in every language. A thing of beauty.

[farzanali]

This is really cool, I've always wondered how it adds up to 180° now i know 😃

[hamadeliterank]

Please make more of these!! We really love it!

[uauausuuahshauaiausuuaususu]

The Song: Shake
Presh: Continues to wiggle the triangle

[VD]

The formula for shapes angle sum is 180(n-2)
n is the number of sides, so if it was a pentagon you would do 5-2, which is 3, and then multiply that by 180, which makes 540. So the sum of the angles in any 5 sided shape is 540.

[mihirchakradeo]

I'm so grateful to you for posting this...
Thanks a lot.

[鈴木悠真-nz]

Demonstrated the sum of angles geometric proof and still applies use one of the angle is obtuse. Cool animation!!!

[kskmathzone]

Sir excellent. Which app do you use for this animation

[galacticwarrior.]

song is called "jump in the line" if anyone's asking :)

[onradioactivewaves]

Thank goodness I woke up in Euclidean space today

[marcusscience]

This generalises to any polygon, for an n-agon the interior angles add up to (n-2)π, simply because you can cut an n-agon into (n-2) triangles.

[stalthyone]

I don’t understand why some people have such a hard time grasping this concept. It’s so simple.

[moonbek_]

The best way explanation which I have ever seen during my life❤

[nomadshooter]

THANK YOU!!! I've been thinking about this for days and I kept forgetting to look it up

[kemalsahbegovic]

BROOO THANK YOU SOLVE ALLLL THERE SHOULD BE MORE CHANELLLSSSS LIKE THISSSS❤❤❤

[memarysarkar]

If Euler, Newton, Euclid, Leibniz, Ramanujan were alive today they would have loved this pattern

[comedy_takk]

Maine 90° ka triangle banaya hai🙂
180° wale protector ke jagah 90° wala banaya tha mai🙂

[AbhishekMOfficial]

Such a Nice Animation.
Triangle Dance.😍🤩

[marshiemaaz]

I think it would work as long as that line you'll gonna add is parallel to any line of the triangle (?)