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.
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 🧮
- Find the hypotenuse of a triangle with legs 6 and 8.
- 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: