How to Prove Pythagoras' Theorem is True for All Right Angle Triangles

In this video we cover some pure maths as we look at how to prove Pythagoras' Theorem is true for all right angle triangles. We'll use some reasonably simple algebra to prove that this calculation is true .

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[no_short_circuit]

Joe, I'm like you and love maths. I used to argue at school that English Interpretation was just that but maths is always a true or false for me!. I'm forwarding this to my Grandson to get him to listen to the first couple of minutes, if he watches it all it'll be a bonus.

[tonypybus]

Great Video!! I wish I had had you as a maths teacher. I have always struggled with maths. I am also the inquisitive type and that annoying kid that would also ask why? My secondary school teachers (and I have had many) have to my frustration replied "because it does". Later when I was doing electronics and getting involved with resonant circuits and dealing with integration and differentiation that really did my head in. I always got through the maths element by the skin of my teeth and was always glad to move on to the physical principles and the practical side of my courses.

[cadewilder]

Good video Joe. You made it easy to understand!

[paulmcconnell]

Joe your a great teacher, always struggled with Maths in school. You have a real skill in explaining subjects, especially Maths. I'm relying on your videos to get me through my 2365.Thank you.

[markrowland]

Great video, Joe. Perhaps to be completely rigorous, you should have proved that the inner quadrilateral was actually a square. I was never brilliant at maths, only getting a C at A Level and then struggling with the high maths content of my engineering degree. But even though I find it hard, I do think it's beautiful.

[matthaddock]

Great video Joe. Always thought you explained the subject well.. Best of luck

[RWATraineeElectrician]

Great video Joe, since I've decided to re-train as an electrician, my interest in maths has been rekindled, even though I was rubbish at school 👍

[Paul_Holmes]

Brilliant video Joe, wish I had you at school all those years ago!

[scylam]

Great video Joe, thank you so much for taking the time and doing it step by step, my kids will love it. Very cool indeed. Appreciate that very much. 🙏

[John_]

So has Eddie Woo changed into Joe, or vice-versa? :)

[awt]

There is a bit of proof detail that you have skipped over, which is how you know that the shape in the middle is a square (4 right angle corners), as opposed to a diamond (2 pairs of equal opposite angles). It's of course quite straightforward geometry:

- angles in a triangle add up to 180d; since one of the angles is 90d, you know that the two acute angles in the triangle add up to 90d.
- at the points where two triangles meet, you have three angles which add up to 180d
- two of those are the angles from the triangle, one is the angle from the internal shape

Since the angles from the triangle add up to 90d, the angle from the internal shape must be 90d, hence the internal shape is a square, QED.

[venusflytrap]

But you now need to prove the area of a right angle triangle is a*b/2 and the area of square is a*b joking.