The Pythagorean Theorem is one of the most famous theorems in mathematics. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Proof of the Pythagorean Theorem

There are several proofs for this theorem. One of the most well-known proofs is based on the area of squares.

  1. Area of Squares Method
    • Consider a right-angled triangle with sides a, b, and hypotenuse c.
    • Construct squares on each of the sides a, b, and c.
    • The area of the square on the hypotenuse c is c^2.
    • The area of the square on side a is a^2, and the area of the square on side b is b^2.
    • The total area of the three squares is a^2 + b^2 + c^2.
    • However, this total area can also be represented as the sum of the areas of the two smaller squares and the square on the hypotenuse.
    • Therefore, a^2 + b^2 + c^2 = a^2 + b^2 + c^2.
    • This implies that a^2 + b^2 = c^2.

For more detailed proofs and explanations, you can visit our Mathematics section.

Additional Information

  • The Pythagorean Theorem is not only a mathematical concept but also has practical applications in various fields such as engineering, architecture, and physics.
  • The theorem is named after the ancient Greek mathematician Pythagoras, who is believed to have first discovered it.

Pythagorean Theorem Diagram