The sets of numbers 3, 4, 5 and 5, 12, 13 are examples
of Pythagorean triples. Use what you know about the
Pythagorean theorem to explain why these numbers are called
Pythagorean triples.

Determine whether the following sets of three numbers are
rythagorean triples. Write yes or no for each set of numbers.
8, 15, 17
15, 20, 25
20, 48, 52
2, 9, 11
39, 80, 89

Step-by-step explanation:

The squares of the three numbers in each of the given triples are listed. When the sum of the first two numbers is equal to the third, the set of numbers in the triple is a Pythagorean triple.

  {64, 225, 289}, yes

  {225, 400, 625}, yes — a 3,4,5 triple multiplied by 5

  {400, 2304, 2704}, yes — a 5,12,13 triple multiplied by 4

  {4, 81, 121}, no*

  {1521, 6400, 7921}, yes.

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* the smallest set of integers that is a Pythagorean triple is {3, 4, 5}. The number 2 in this group tells you this cannot be a PT.