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How to Explain the Pythagorean Theorem

The Pythagorean theorem describes how to find the length of the side of a right triangle (a triangle that has a 90-degree angle, also known as a right angle). The theorem is "a2 + b2 = c2," where "a" and "b" are the two regular sides and "c" is the hypotenuse (the side opposite the right angle). Explaining the Pythagorean theorem to students should involve working the formula backward and forward until they understand how this important formula works.

Instructions

- 1
  Work the formula to find the hypotenuse. Give students the measurement of the two sides ("a" and "b") and have them solve for the hypotenuse ("c").
- 2
  Demonstrate how it can be used to find one of the sides. If you know the hypotenuse and one of the sides, the Pythagorean theorem can be used to find the missing side. For example, if you know one side is 5 and the hypotenuse is 13, set the equation up to be 5(squared) + b2 = 13(squared). When solved out, students find that b = 12.
- 3
  Give examples of common Pythagorean triples. Certain sets of numbers should be memorized by students because they are example of whole numbers that work in the Pythagorean theorem (as opposed to giving irrational numbers, which are unsimplified square roots). Examples include "3, 4, 5," "7, 24, 25" and "11, 60, 61."

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