Pythagoras' Theorem

Pythagoras' Theorem describes a fundamental relationship between the three sides of a right-angled triangle. A right-angled triangle is a triangle that contains one angle exactly equal to 90 degrees (a right angle). The side opposite this right angle is the longest side of the triangle and is called the hypotenuse. The other two sides, which meet at the right angle, are called the legs or catheti (singular: cathetus). The theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs. If we label the legs as a and b, and the hypotenuse as c, the theorem can be written as: a² + b² = c². This is the most common algebraic representation. It is important to understand that this relationship holds only for right-angled triangles. It does not apply to acute or obtuse triangles. The theorem can be used in two main ways: