**Question: **What Is the Pythagorean Theorem?

**Answer: **We use the Pythagorean Theorem when we want to know the remaining length of the side of a right triangle for which we already know two lengths.

The Presocratic philosopher Pythagoras is given credit for some mathematical principles, including Pythagorean Numbers and the Pythagorean Theorem.

The Pythagorean Theorem states that sum of the squares of the lengths of the two sides of a right triangle (sides a and b) will equal the square of the length of the hypoteneuse (c). Pythagorean triples are three integers that satisfy the condition of a² + b² = c² (3, 4, and 5 satisfy this equation). The name of Pythagoras was selected for this theorem not because he discovered it -- the Pythagorean theorem or Pythagorean triples had been in use for centuries. -- but perhaps because Pythagoras was the first to prove the theorem. The Pythagorean Theorem and Pythagrean Triples are related.

You can demonstrate for yourself with graph paper. Take a piece of graph paper that is 3 squares by 3 squares, another that is 4 squares by 4 squares, and a third that is 5 squares by 5 squares; put them together so they form a right triangle in their middle. It will also work if you double the numbers (6², 8², 10² --> 36 + 64 =100).

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