The Pythagorean Theorem is a mathematical rule that explains the relationship between the sides of right triangles. According to this rule: In a right triangle, the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.

This statement is valid only for right-angled triangles. Mathematically, it is written as:

c² = a² + b²

Where:

c = hypotenuse (the longest side)

a and b = the other two sides

^{Pythagorean Theorem (Created with Artificial Intelligence.)}

What is a Right Triangle?

If one of the angles in a triangle is exactly 90 degrees, this triangle is called a right triangle. This 90-degree angle is called a right angle. The long side opposite the right angle is called the hypotenuse, while the other two sides are called the legs of the right triangle.

How Does the Pythagorean Theorem Work?

The easiest way to understand the theorem is to start with an example. If the sides of a right triangle are 3 and 4 units, then the hypotenuse will be 5 units.

Because:

3² + 4² = 9 + 16 = 25 → 5²

This example is the most well-known form of the Pythagorean Theorem. This triangle is also called the “3-4-5 triangle.”

Where Is It Used?

The Pythagorean Theorem is useful not only in school but also in real life. Some areas of use are:

Measuring the height of buildings

Map drawing

Engineering designs

Navigation calculations for airplanes and ships

History of the Pythagorean Theorem

The theorem is named after the ancient Greek philosopher and mathematician Pythagoras. Pythagoras lived about 2,500 years ago. However, this theorem was known long before him! The Egyptians and Babylonians used this relationship in their constructions. The 3-4-5 triangle in particular is the most well-known example.

^{Pythagorean Theorem (Created with Artificial Intelligence.)}