Study Guide

Basic Geometry - Pythagorean Theorem

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Pythagorean Theorem

A long time ago, in ancient Greece, a brilliant guy named Pythagoras discovered something pretty amazing and useful.

Pythagorean Theorem: a2 + b2 = c2

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Pythagorean abc

  • Legs (a and b): the sides of the triangle adjacent to the right angle. They don't need to be the same length in order for this theorem to work.
  • Hypotenuse (c): the side of the triangle opposite the right angle which, conveniently, is always the longest side.

Right Triangles

So, let's break this down. If you square each side of the triangle, the sum of the areas of the two legs squared is equal to the hypotenuse squared.

Pythagorean Image

Here you can see it with numbers:

Pythagorean with numbers

The area of the two smaller squares is (3 × 3 = 9 cm2) and (4 × 4 = 16 cm2).

The area of the larger square is equal to (5 × 5 = 25 cm2).

If you add the two smaller areas together, you get the area of the square of the hypotenuse (9 + 16 = 25 cm2).

Look Out: Do not attempt this with obtuse or acute triangles. This awesome theorem only works for right triangles.

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