Pythagoras’ Theorem

Over 2000 years ago there was an amazing discovery about triangles, Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras (c. 570–495 BC) as it is he who, by tradition, is credited with its first recorded proof.
Pythagoras studied right triangles, and the relationships between the legs and the hypotenuse of a right triangle, before deriving his theory.

When a triangle has a right angle (90°) ...
... and squares are made on each of the three sides, ...

... then the biggest square has the exact same area as the other two squares put together!

Pythagoras
It is called "Pythagoras' Theorem" and can be written in one short equation:
a2 + b2 = c2
pythagoras squares a^2 + b^2 = c^2
Note:
  • c is the longest side of the triangle
  • a and b are the other two sides

Definition

The longest side of the triangle is called the "hypotenuse", so the formal definition is:
In a right angled triangle:
the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
The animated picture of this theorem is given below,

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