The Pythagorean Theorem is a fundamental principle in Euclidean geometry, relating the sides of a right-angled triangle. It states that:

In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Formula: $ a^2 + b^2 = c^2 $

Key Concepts 🔍

  • Right Triangle: A triangle with one 90° angle.
  • Hypotenuse: The longest side, opposite the right angle.
  • Legs: The two shorter sides forming the right angle.
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Applications 📈

  • Calculating distances in 2D space
  • Solving real-world problems (e.g., ladder against a wall)
  • Verifying if a triangle is right-angled

Example:
If $ a = 3 $ and $ b = 4 $, then $ c = \sqrt{3^2 + 4^2} = 5 $.

Practice Problems 🧮

  1. Find the hypotenuse of a triangle with legs 6 and 8.
  2. A 10m ladder leans against a wall, reaching 8m up. How far from the wall is the base?

Learn More 🌐

For deeper insights into triangles:

Right_triangle_