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Pythagoras Theorem

If the triangle had a right angle (90°), and you made a square on each of the three sides, then the biggest square had the exact same area as the other two squares put together.

pythagoras-theorem1
It is called “Pythagoras Theorem” and can be written in one short equation: \(a^2 + b^2 = c^2\)

Definition:

In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

pythagoras-theorem2

Let’s see if it really works using an example.

Pythagoras Theorem Example:

A “3,4,5” (pythagorean triple) triangle has a right angle in it.

pythagorean-theorem-example

Let’s check if the areas are the same:
\(3^2\) + \(4^2\) = \(5^2\)
Calculating this becomes:
9 + 16 = 25.

If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)

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