This is the Pythagorean Theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two side
s. In mathematical terms, it can be expressed as:
c² = a² + b²
Where:
- c represents the length of the hypotenuse (the side opposite the right angle)
- a and b represent the lengths of the other two sides (known as the legs or catheti)
This theorem is fundamental in geometry and has numerous applications. It allows us to calculate the length of any side of a right-angled triangle if the lengths of the other two sides are known. Additionally, it helps us determine whether a triangle is right-angled or not.
The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is often credited with its discovery. However, evidence suggests that this theorem was known and used by civilizations before Pythagoras, such as the Babylonians and Egyptians.
The Pythagorean Theorem forms the basis for trigonometry, as it relates the lengths of the sides of a right triangle to its angles. It is also utilized in various fields such as architecture, engineering, physics, and astronomy, where right-angled triangles are commonly encountered.
Overall, the Pythagorean Theorem is an essential tool in mathematics, enabling us to understand and solve problems involving right-angled triangles and their properties.