The Pythagorean Theorem is a mathematical formula that describes the relationship between the three sides of a right triangle. It states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides.
In other words, if a right triangle has sides of length a and b, and a hypotenuse of length c, then the Pythagorean Theorem can be expressed as the following equation:
```
a^2 + b^2 = c^2
```
The Pythagorean Theorem is one of the most important and fundamental theorems in mathematics. It has been used to solve problems in geometry, trigonometry, and other areas of mathematics for centuries. It is also used in many real-world applications, such as surveying, construction, and navigation.
Here is a simple example of how to use the Pythagorean Theorem:
Suppose you have a right triangle with sides of length 3 and 4. You want to find the length of the hypotenuse.
Using the Pythagorean Theorem, we can write the following equation:
```
3^2 + 4^2 = c^2
```
Solving for c, we get:
```
c^2 = 9 + 16 = 25
```
Taking the square root of both sides, we get:
```
c = 5
```
Therefore, the length of the hypotenuse is 5.
The Pythagorean Theorem is a powerful tool that can be used to solve a variety of problems. It is a foundational theorem in mathematics and has many real-world applications.
