Pythagorean Theorem & Its Inverse (my favorite proof)

I'll be sharing my favorite proof of the Pythagorean Theorem and its inverse, using similar triangles. The Pythagorean Theorem is a fundamental concept in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. But why does this theorem hold true? In this video, I'll walk you through a simple and elegant proof that uses similar triangles to demonstrate the Pythagorean Theorem and its inverse. By understanding how the ratios of the sides of similar triangles relate to each other, we can prove this theorem and its inverse with ease. Whether you're a math enthusiast or just curious about the Pythagorean Theorem, this video is for you.

This question was asked by Toby from my Chinese channel:

@blackpenredpen

[renegado]

Omg spiderman is supporting your channel!! You're going to be at 400k subscribers by the end of the year for sure

[nathangreene]

This is far clearer and more straight-forward than the traditional proofs.

[jacoboribilik]

The inverse pythagorean theorem is some serious beautiful shit.

[David-wwsg]

Wow, I've never seen the inverse Pythagoras Theorem. Love your proof videos!

[FACH-nrjz]

I love math so much! Thank you so much for this video. For Pythagoras, as soon as you drew the vertical height, h, I decided to try to do the proof and I did it. I also just happen to label the parts of c as c1 and c2 also lol. For the inverse, I knew what was going to happen as you were going and it was beautiful! The simplicity of math can be so great; I just wish schools showed it the right way.

[idavid]

My favorite proof of the Pythagorean theorem is Garfield's (the president, not the cat) proof, just because of how clever it is.

[viletomedoze]

Awh the nostalgia. This video hit me in the heart. It's amazing how far we've come from counting numbers to algebra and to functions and calculus and to complex. I remember not understanding the Pythagorean theorem and back then trigonometry was like the real deal.

[Awesome]

Loved the inverse proof, and also this is now my favourite proof as it uses similar triangles which is neat!

[HerrHoldem]

Cool! Thank you!
This proof doesn't ask for special math knowledge, just fundamental ones.

I have done it, but in different way:
I use sin and cos in my proof. After I finished, I have understood that sina^2 + cosa^2 = 1 is also Pythagorean theorem and I used Pythagorean theorem in my proof of Pythagorean theorem 👌

The Inverse Pythagorean theorem is really useful, I think

[migueld]

I wish they taught this proof in schools to teach kids things don't just come out of the blue.

[dicksonphisthur]

Really pleased to see the inverse proof. And who, I wonder, are the four people who don't like this video?

[brahimtchouk]

What a simple proof, you Chinese, have turned the world upside down.you have unearthed everything.you are amazing.

[keithmasumoto]

omg, I love that inverse to get the height from the hypot. Very nice, thank you!

[gianfrancosavino]

beautiful. the proof based on triangles similarity is really elegant.

[shreyassinha]

The inverse is too beautiful, I remember that elegance after deriving it myself :)

[mateszabo]

They say the pythagorean theorem have 50 proof, but from now on ur first proof is my favorit.

[josephbrandenburg]

I like your videos because I can see that you're genuinely excited about the maths. There's a million people out there that understand it well enough to explain it, but it's a good video because you love it.

[numbo]

Love how you tackle really hard and also simpler problems with the same enthusiasm!

[geekysibi]

This is the first proof I loved... Like we use it every day and it's fun

[mokouf]

Proof by area, really straightforward.