Proof without words that the angles of a triangle sum to 180 degrees

Rotating by the three angles of a triangle amounts to half of a complete revolution, or 180 degrees.

I couldn't find a good visual of this so I made this and thought it was neat.

[pizzaTimePedro]

absolutely love this explanation! So simple and subtle and I can even imagine how adding a 4th point will sum to 360 degrees! Well done mate!

[buddy]

At first I thought it was just a meme that doesn't actually explain anything, and then it hit me. Great proof

[Cecilia-kyuw]

I'm interpreting this as proof by revolution.



Edit: I'm having a crisis over the fact different sides are used, rendering the proof neutralised until that's resolved.

[CapeBone]

I take exception to this because the animation demonstrated that one trip around the triangle resulted in the stick being oriented the opposite way. Thus, two trips around the triangle resulted in the stick being oriented the original way.

This result would also be achieved with any closed polygon with an odd number of sides.

We can conclude that the sum of angles in a triangle -- or any closed polygon with an odd number of sides -- is an odd number times the total angle in a circle over 2.

Is there some other detail I'm missing?

[_mrnelson_]

This is closer to a demonstration than a proof. But I still like it.

[HEA]

Why does everyone understand that?!!?! I see some stick sliding on triangle sides and its please explain

[carlossaliba]

i think im just too stupid to understand this

[Ckazochnik_Iz_Moskvi]

*Rotating by the three angles of a triangle amounts to half of a complete revolution, or 180 degrees.*
POV: France ☠💀


Btw this is really good explanation

[michaellong]

for the record though if we really want to be annoying, this is only one triangle

[brycesmith]

Took me a momemt to realize this wasn't a meme😂

[TommyTommy]

But how do we deduce that this can be applied to every triangle?

[kxhu]

thats pretty neat, had to think for some seconds but seeing the line ending up at +180 degrees of when it started is a good explanation

[throwawayavclubber]

This only proves that triangles have an odd number of sides.

[adrien]

Simple and efficient. I wonder what the greeks would have thought of that.

[karans]

Nice! Now do it with every triangle :)

[ryku]

Angle sum of polygon= (no. of sides-2)*180

[icephoenix]

this needs a 10 hour loop lol
(also INCREDIBLE VISUAL PROOF I would've never thought of this myself)

[Shailendra]

For those who don't get it: look at the coloring of the moving rod. It starts with the blue side down, when it makes its way within the triangle.

The first way around the triangle, it ends up with the purple side down. The second time around the triangle, the rod finally ends up with the blue side down, as from the start of the video.

What this tells us is the following: in order to make a full way around something, the starting point has to exactly be the ending point, like a full circular motion. In a circle, to go all the way around means you rotate a full 360 degrees. Now, this means that the rod in the video, after moving inside the triangle, ALSO has to end up be exactly in the same color position at the bottom of the triangle (as it started with), for it to have made a full 360 degrees, 'circular' motion.

Since it takes two runs for the rod to reach this (and the pathway within the triangle is the same for each run), therefore the amount of degrees that the rod has passed inside the triangle after ONE triangular run, would be 360/2 = 180 degrees. And this correlates with the total amount of degrees within a triangle.

[NfIsTheBestOpening]

this proof is really good however if there were curves on the edges wouldnt it still do that?

[francogonz]

Gorgeous! I have to look at comments to understand. It's that simple that looks like a dank meme😂.

I call this: Dank Proof