Pythagorean theorem, geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. Although the theorem has long been associated with the Greek mathematician Pythagoras, it is actually far older. The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle. Pythagoras (Pythagorean) Theorem explains the relationship between the three sides of a right-angled triangle. It helps us find the length of a missing side if the other two sides are known. What is the Pythagorean theorem & what is it used for – learn how to solve it with equation, proofs, real-life examples, solved problems, and diagram The Pythagorean theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Learn about the Pythagorean theorem in geometry. Get its definition, formula, and worked example math problems. What is the Pythagorean Theorem? The Pythagoras theorem is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse. The Pythagoras theorem is algebraically written as: a 2 + b 2 = c 2 Pythagoras. Over 2000 years ago there was an amazing discovery about triangles: When a triangle has a right angle (90°). Definition of Pythagorean Theorem For a given right triangle, it states that the square of the hypotenuse, $c$, is equal to the sum of the squares of the legs, $a$ and $b$. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points.