The Pythagorean Theorem Explained The Pythagoras Theorem is a fundamental theorem in geometry that relates the sides of a right triangle. It states that...
The Pythagoras Theorem is a fundamental theorem in geometry that relates the sides of a right triangle. It states that in any right triangle, the square length of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
Formally, the theorem can be stated as:
In any right triangle with sides a, b, and c, where c is the hypotenuse, then:
c² = a² + b²
Here's how this formula helps us find the length of the hypotenuse:
We know that the square length of the legs (a and b) add up to the square length of the hypotenuse. So, c² = a² + b².
This means that the hypotenuse is the longest side in the triangle and is always greater than the other two sides.
Additionally, the Pythagorean theorem ensures that the hypotenuse will always be the longest side in any right triangle.
Examples:
a = 3 cm
b = 4 cm
c = 5 cm
The Pythagorean theorem then tells us that:
c² = a² + b²
5² = 3² + 4²
25 = 9 + 16
c = 13 cm
Therefore, the length of the hypotenuse is 13 cm, which is consistent with the Pythagorean theorem.
The Pythagorean theorem has wide applications in geometry and other fields. It is used to solve problems involving right triangles, calculate distances, and determine properties of geometric shapes