# Prove Pythagorean Theorem

Discussion in 'Algebra' started by nycmathguy, Jul 6, 2022.

1. ### nycmathguy

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College Algebra
Chapter 1/Section 3

Prove the Pythagorean Theorem. Explain each step along the way.

nycmathguy, Jul 6, 2022
2. ### MathLover1

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The Pythagorean Theorem says that, in a right triangle, the

a^2 + b^2 = c^2

Proof:

We can show that a^2 + b^2 = c^2 using Algebra

Take a look at this diagram:

it has that "abc" triangle in it (four of them actually):

It is a big square, with each side having a length of a+b, so the total area is:

A = (a+b)(a+b)

Now let's add up the areas of all the smaller pieces:

First, the smaller (tilted) square has an area of: c^2

Each of the four triangles has an area of: ab/2

So all four of them together is: 4ab/2 = 2ab

Adding up the tilted square and the 4 triangles gives: A = c^2 + 2ab

The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:

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

NOW, let us rearrange this to see if we can get the Pythagoras theorem:

Expand (a+b)(a+b): a^2 + 2ab + b^2 = c^2 + 2ab

Subtract "2ab" from both sides:

a^2 + b^2 = c^2 DONE!

MathLover1, Jul 6, 2022
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3. ### nycmathguy

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Wow! You went beyond with this reply.

nycmathguy, Jul 6, 2022