A theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides

What is the Pythagorean Theorem?
The Pythagorean Theorem is a fundamental principle in geometry that relates to right-angled 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.
Formula
- The theorem can be expressed with the formula:
c² = a² + b²
where:
- c = length of the hypotenuse
- a and b = lengths of the other two sides
Understanding the Components
- Right Triangle: A triangle with one angle measuring 90 degrees.
- Hypotenuse: The longest side of the triangle, opposite the right angle.
- Legs: The other two sides that form the right angle.
Application of the Theorem
- Distance Calculation: It helps in finding the distance between two points in a plane.
- Real-Life Situations: Used in construction, navigation, and various fields of engineering.
Visual Representation
- Imagine a right triangle. You can visualize it with the two legs forming a right angle and the hypotenuse stretching across. Using the theorem, if you know the lengths of the legs, you can easily calculate the hypotenuse.
Conclusion
The Pythagorean Theorem is an essential tool in mathematics, providing a method to calculate distances and relationships in geometric figures. Understanding this theorem is crucial for progressing in geometry and its applications in real-life scenarios.