What is Pythagoras' Theorem?

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Pythagoras' Theorem is a fundamental principle in geometry, named after the ancient Greek mathematician Pythagoras. It applies specifically to right-angled triangles, which are triangles that have one angle measuring 90 degrees. The hypotenuse is the side opposite the right angle and is the longest side of the triangle. The other two sides are referred to as the 'legs' of the triangle.

The theorem can be expressed with the formula: \(a^2 + b^2 = c^2\), where \(c\) represents the length of the hypotenuse, and \(a\) and \(b\) represent the lengths of the other two sides. For example, if one leg of a right-angled triangle is 3 units long and the other leg is 4 units long, you can use Pythagoras' Theorem to find the length of the hypotenuse. According to the theorem, \(3^2 + 4^2 = c^2\), which simplifies to \(9 + 16 = 25\), so \(c = \sqrt{25} = 5\).

This theorem is incredibly useful in various real-world applications, such as construction, navigation, and even in computer graphics. It helps in determining distances and ensuring structures are built correctly. Understanding Pythagoras' Theorem is essential for solving many problems in GCSE Maths, and it forms the basis for more advanced topics in trigonometry and geometry.