## Pythagorean Theorem

### The Pythagorean Theorem is a fundamental concept in mathematics that relates to right triangles

The Pythagorean Theorem is a fundamental concept in mathematics that relates to right triangles. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In mathematical terms, if a and b are the lengths of the two legs of a right triangle, and c is the length of the hypotenuse, the Pythagorean Theorem can be expressed as:

a^2 + b^2 = c^2

This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It has far-reaching applications in various areas of mathematics, physics, engineering, and even in everyday life.

The Pythagorean Theorem allows us to calculate the length of an unknown side of a right triangle when the lengths of the other two sides are known. It can also be used to determine if a triangle is a right triangle by checking if the equation holds true for the given side lengths.

For example, if we have a right triangle with one leg measuring 3 units and the other leg measuring 4 units, we can use the Pythagorean Theorem to find the length of the hypotenuse. Plugging the values into the equation, we get:

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

Taking the square root of both sides, we find that c = 5. Hence, the length of the hypotenuse in this triangle is 5 units.

The Pythagorean Theorem is a powerful tool that helps us investigate the relationships between the sides of right triangles and has extensive applications in geometry and beyond.

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