Is this equivalent to the Pythagorean Theorem?

In summary, the conversation is about the Pythagorean theorem and a question is raised about a statement on the webpage. The statement is clarified as a representation of the theorem using lengths between points.
  • #1
Quine!
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So I was reading up on the Pythagoreans, and I came across this page: http://www.math.ufl.edu/~rcrew/texts/pythagoras.html .

I don't see the reasoning behind this statement.

"Since AB=AD+DB, adding these equations yields

A(B2)=A(C2)+C(B2)
which is the Pythagorean theorem."


I tried some simple algebra on this statement and couldn't get Pythag to fall out of it. Can someone figure out a derivation for this?
 
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  • #2
That's not what the page says. It says,

[tex]AB^2 = AC^2 + CB^2[/tex]

A, B, and C are not variables. [itex]AB[/itex] represents the length between points A and B. You should read [itex]AB^2[/itex] as a single length being squared.
 

Related to Is this equivalent to the Pythagorean Theorem?

1. Is the Pythagorean Theorem the same as the Law of Cosines?

No, the Pythagorean Theorem only applies to right triangles, while the Law of Cosines applies to any type of triangle.

2. Can the Pythagorean Theorem be used for non-right triangles?

No, the Pythagorean Theorem only applies to right triangles and cannot be used for non-right triangles.

3. Is the converse of the Pythagorean Theorem always true?

No, the converse of the Pythagorean Theorem states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle. This statement is not always true.

4. What is the Pythagorean Theorem used for?

The Pythagorean Theorem is used to find the length of a missing side in a right triangle when the lengths of the other two sides are known.

5. Can the Pythagorean Theorem be used in higher dimensions?

Yes, the Pythagorean Theorem can be extended to higher dimensions, where it is known as the Pythagorean Theorem for n dimensions.

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