Pythagorean Theorem

Definition of Pythagorean Theorem

    A set of three non-zero numbers whose sum of the squares of two numbers is equal to the square of the third number.

More About Pythagorean Theorem

  • If a, b, c ? 0, and a2 + b2 = c 2, then (a, b, c) is called a Pythagorean triple.
  • Measures of a Pythagorean triple make a right triangle.
  • If a, b, and c form a Pythagorean triple, then for any positive number n, na, nb, and nc also form a Pythagorean triple i.e. if 3, 4, and 5 form a Pythagorean triple, then 3(3, 4, 5) i.e. 9, 12, and 15 also form a Pythagorean triple.

Video Examples: Pythagorean triples


Example of Pythagorean Theorem

    A set (5, 12, 13) is a Pythagorean triple.
    52 + 122 = 25 + 144 = 169
    132 = 169

Solved Example on Pythagorean Theorem

Ques: Which of the following is a Pythagorean triple?

    Choices:
    A. 6 m, 8 m, 10 m
    B. 5 m, 7 m, 9 m
    C. 6 m, 7 m, 8 m
    D. 5 m, 6 m, 7 m
    Correct Answer: A

Solution:

    Step 1: Pythagorean triples are a set of three integers a, b, c, which form the measures of the sides of a right-angled triangle.
    Step 2: If the given measures satisfy the condition, c2 = a2 + b2, then the measures make a right triangle.
    Step 3: Here, the measures 6 m, 8 m, and 10 m satisfy the condition. (102 = 62 + 8 2 ? 100 = 36 + 64 = 100)
    Step 4: Thus, the measures 6 m, 8 m, and 10 m make a right triangle and thus it is a Pythagorean triple.