In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle ) is equal to the sum of the areas of the squares on the other two sides.

2020年5月4日 · What is the Pythagorean Theorem? The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared. You might recognize this theorem in the form of the Pythagorean equation: \[ a^{2} + b^{2} = c^{2} \]

Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia.

2025年3月21日 · Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a 2 + b 2 = c 2.

Introduction to the Pythagorean Theorem Page 2 Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle equals the square of its hypotenuse. In other words, a2 + b2 = c2; where aand bare the lengths of the two legs and cis the length of the hypotenuse. a b c Example 2.

It is the "Pythagorean Theorem" and can be written in one short equation: a 2 + b 2 = c 2. Note: c is the longest side of the triangle; a and b are the other two sides; Definition. The longest side of the triangle is called the "hypotenuse", so the formal definition is:

Use the Pythagorean theorem to determine the length of X. Identify the legs and the hypotenuse of the right triangle. The legs have length 6 and 8. X X is the hypotenuse because it is opposite the right angle. Substitute values into the formula (remember 'C' is the hypotenuse). A2 + B2 = C2 62 + 82 = X2 A 2 + B 2 = C 2 6 2 + 8 2 = X 2.

The Pythagorean Theorem relates the three sides in a right triangle. To be specific, relating the two legs and the hypotenuse, the longest side. The Pythagorean Theorem can be summarized in a short and compact equation as shown below.

2024年6月8日 · The Pythagorean Theorem, also known as Pythagoras theorem is a mathematical relation between the 3 sides of a right triangle, a triangle in which one of 3 angles is 90°. It was discovered and named after the Greek philosopher and mathematician of Samos, Pythagoras.

The Pythagorean theorem states that if a triangle has one right angle, then the square of the longest side, called the hypotenuse, is equal to the sum of the squares of the lengths of the two shorter sides, called the legs.