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  • 1. The Pythagorean Theorem - 9.2
    • Objectives:
    • Prove the Pythagorean Theorem
    • Use Pythagorean to solve problems
  • 2. Pythagorean Theorem
    • In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
    • c 2 = a 2 + b 2
    a b c
  • 3. Proving Pythagorean
    • Look at page 535
  • 4. Using Pythagorean
    • A Pythagorean triple is a set of 3 positive integers a, b, and c that satisfy the equation c 2 = a 2 + b 2
    • 3, 4, and 5 are an example.
  • 5. Using Pythagorean
    • If the legs are 5 and 12, what is the hypotenuse?
    • 5*5 + 12*12 = 25 + 144 = 169
    • √ 169 = 13
    • 5, 12, and 13 are Pythagorean triples.
  • 6. Find the length of the hypotenuse:
    • x 2 = 5 2 + 12 2
    • x = √25 + 144
    • x = 13
    x 5 12
  • 7. Find the length of the leg:
    • 14 2 = 7 2 + x 2
    • 196 = 49 + x 2
    • 147 = x 2
    • x = 7√3
    14 7 x
  • 8. Find the area of a triangle:
    • Find the height:
    • 7 2 = 5 2 + h 2
    • 49 = 25 + h 2
    • 24 = h 2
    • h = √24
    7 m 7 m 10 m
  • 9. Find the area of a triangle:
    • Now find the Area: A = 1/2 b*h
    • A = 1/2 * 10 * √24
    • A = 24.5 m 2
    7 m 7 m 10 m
  • 10. Now do Example 4, p. 537
  • 11.
    • Pythagorean video
  • 12. Homework
    • Do worksheets.