[Warning: This post is quite basic, I mean really basic!]
In an earlier post, we saw a proof without words. On this post we'll see another proof without words. I really loved this when I saw it for the first time and I hope you do too.
Today's topic is really simple: the sum of the angles of a triangle.
We all know that the sum of the angles of any triangle is equal to . We've all learned how to prove that in school.
Some of you probably tore off the corners of a triangle to verify that in some point in your life [if you haven't done this, try it now!].
But on this post, we're going to do it in a different way, a way that [hopefully] makes us appreciate the beauty in the simplest of things. Let's get on with it!
We're going to start with a question? What does it mean when you rotate some thing by ? If we had a pencil lying horizontally and if we rotated it by , what would happen?
The picture above demonstrates what a rotation by looks like. Keep that in mind.
We're going to start by drawing a triangle and putting a pencil horizontally below it.
We have to prove that .
We're going to start by rotating the pencil by .
Then by ...
And finally, by ...
Now if you compare how the pencil was before rotation and what it looks like after being rotated by the angles of triangle , you'll see that the pencil has rotated exactly by .
So, [Proved without words!].
This just goes to show that you can look at the simplest of things from a different perspective and enjoy the beauty in them.
Now using the same principle, prove to yourself that the sum of the internal angles of a quadrilateral equals . Turn the pencil around!