Introduction to the Pythagorean Theorem

Overview

• Subject: Pythagorean Theorem
• Presenter: Mr. Jay
• Focus: Right triangles and the relationship between their sides
• Named After: Pythagoras, a Greek philosopher and mathematician

Basics of the Pythagorean Theorem

• Applies to: Right triangles only
• Hypotenuse: Longest side of a right triangle, directly opposite the right angle
• Legs: The other two shorter sides of the right triangle
• Formula: a² + b² = c²
  • a and b are legs of the triangle
  • c is the hypotenuse
• Purpose: Use the formula to find the missing side length when two side lengths are known

Example Problem 1

• Given: Legs of 4 feet and 3 feet
• Find: Hypotenuse (c)
• Steps:
  1. Plug values into the equation: 4² + 3² = c²
  2. Calculate: 16 + 9 = 25
  3. Solve for c: √25 = 5
  4. Result: Hypotenuse (c) = 5 feet

Visual Representation

• Right Triangle: Legs = 4 feet and 3 feet, Hypotenuse = 5 feet
• Squares on Each Side: Take squares of each side's lengths
  • Area of Leg a: 4² = 16 square feet
  • Area of Leg b: 3² = 9 square feet
  • Area of Hypotenuse c: 5² = 25 square feet
• Conclusion: Sum of the areas of legs' squares equals the area of the hypotenuse's square (16 + 9 = 25)

Example Problem 2

• Given: one leg = 15 cm, hypotenuse = 17 cm
• Find: Missing leg (b)
• Steps:
  1. Plug values into the equation: 15² + b² = 17²
  2. Calculate: 225 + b² = 289
  3. Solve for b: 289 - 225 = 64
  4. Find b: √64 = 8
  5. Result: Missing leg (b) = 8 cm

Summary

• Key Points:
  • The Pythagorean theorem helps find missing sides of right triangles.
  • Equation: a² + b² = c² where c is always the hypotenuse.
  • Visualization involves squaring each side length and comparing areas.

Thanks for watching!