The Pythagorean theorem is a fundamental relationship in Euclidean geometry that deals with the sides of a right triangle. Here's the gist:
In a right triangle:
The square of the hypotenuse (longest side, opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
You can express it mathematically as:
a² + b² = c²
where:
a and b are the lengths of the legs of the triangle.
c is the length of the hypotenuse.
This theorem has numerous applications in various fields, including:
Solving problems in geometry: Finding missing side lengths, proving triangles are right-angled, etc.
Trigonometry: Understanding relationships between angles and side lengths in triangles.
Physics and engineering: Calculating distances, forces, and other quantities.
The Pythagorean theorem is considered one of the most important and well-known mathematical theorems, with a rich history dating back thousands of years.
