Why is the pythagorean Therom only true for right triangles?

Assume a, b, c are the sides of a triangle which is not right, but for which nonetheless a2 + b2 = c2.

Position the sides a and b as to make a right angle. Let d be the distance between their endpoints. By the Pythagorean theorem,
a2 + b2 = d2. Which implies

c2 = d2.

From where, c = ±d. However, both c and d are positive from the context. Therefore, c = d in the first place. Therefore, the original triangle was in fact right.

What's the connection with the Pythagorean Therom area of squares and Pythagorean Triples?

> What's the connection with the
> Pythagorean Therom area of squares
> and Pythagorean Triples?

I do not understand your question.

I want to know how they are all interalted, if it's not too much to ask. What I want to know is how the area of squares applies tothe Pythagorean Therom, and Pythagorean Triples. How they all fit together.

The Pythagorean theorem asserts that the sum of areas of the squares constructed on the legs of a right triangle equals the area of the square built on its hypotenuse.

Between us, I am uncomfortable answering your questions. This is because I get a feeling that my effort - however small - of typing the answers goes nowhere. You have never followed up on your first question, although I did expect you to.

Well, I think that your input that you could give me on to this question would be much greater then any ideas that I could ever come up with, becase your page on proofs for the Pythagorean Therom is truely amazing. Yes, I still am wondering why the Pythagorean Therom is only true for right triangles, becauase I did not understand the frst sentece of your origional response to that question. Any input tht you have would be greatly appreciated. Thank you :)

>Well, I think that your input
>that you could give me
>on to this question would
>be much greater then any
>ideas that I could
>ever come up with,

Not so, as the last sentence in your message shows very clearly. I can waste plenty of time unless you make some effort at trying to understand both your question and my answer.

> becase
>your page on proofs for
>the Pythagorean Therom is truely
>amazing.

Thank you. But this is irrelevant as you apparently did not get the point.

> Yes, I still
>am wondering why the Pythagorean
>Therom is only true for
>right triangles, becauase I did
>not understand the frst sentece
>of your origional response to
>that question.

The first sentence reads:

Assume a, b, c are the sides of a triangle which is not right, but for which nonetheless a2 + b2 = c2.

Which means, "Assume there is a triangle which is not right but for which the Pythagorean theorem holds nonetheless."

What follows afterwards is a demonstration that that assumption leads to a contradiction.

>Any input
>tht you have would be
>greatly appreciated. Thank you
>:)