Explain the Pythagorean Theorem, its proofs, and applications.

Question

Explain the Pythagorean Theorem, its proofs, and applications.

At least one example of correct use of all of the following:

1. Commas
2. Colons
3. Semicolons
4. Exclamations
5. Quote Marks
6. Apostrophes
7. Parentheses
8. Dashes
9. Hyphens
10. Citation in APA format (at least one resource)

Answer 1

The Pythagorean Theorem says

h^2 = a^2 + b^2

the hypotenuse squared = the sum of the squares of the two other sides of a right triangle, the altitude squared + base squared.

It's a special case of the Law of Cosines

c^2 = a^2 + b^2 -2abCosC where C= 90 degrees or pi/2,

c^2 = a^2 +b^2 -2ab(Cos90)

c^2 =a^2 + b^2 -2ab(0)

c^2 = a^2 +b^2

There are 100+ proofs of the Theorem. You can find them on line.

Mostly geometric in nature. Former US President James A. Garfield invented a novel proof when he was in the House of Representatives. His proof is published in math journals and can be found online.

The diagonal of a rectangle = d = the square root of the sum of the sides squared

d^2 = w^2 + l^2

d = square root of (w^2 + l^2) where w=width and l=length of the rectangle.