Pythagorean Theorem – Prove It! Converse of Pythagorean Theorem 1.) Is a triangle with side measures of 30, 40, and 50 units a right triangle? Prove it! Yes, because = 50 2 ( = 2500). (The sum of squares of legs equals square of hypotenuse in a right triangle.) 2.) Is a triangle with side measures of 6, 7, and 12 units a right triangle? Prove it! No, because ≠ 12 2 ( ≠ 144).

Pythagorean Triples A Pythagorean Triple is a set of positive integers, a, b, and c, that fit the rule: a 2 + b 2 = c 2. Copy the definition above and the process for generating Pythagorean Triples and the easy to remember triples into your notebook from the following slides.

Pythagorean Triples Generating a Pythagorean Triple is as easy as A, B, C. This process gives a triple with the difference of 1 between the hypotenuse and the longer leg. The process is as follows: A.) Pick an odd positive integer. B.) Square it. C.) Determine consecutive integers whose sum equals B (divide B by 2 and take the 2 integers on either side of the answer). D.) You have generated a triple with A and C.

Pythagorean Triples Follow the process: A.) Pick an odd positive integer. B.) Square it. C.) Determine consecutive integers whose sum equals B (divide B by 2 and take the 2 integers on either side of the answer). D.) You have generated a triple with A and C. Example: & 25 7, 24, 25 Example: & 61 11, 60, 61

Pythagorean Triples Other easy to remember Pythagorean Triples are: 3, 4, 5 6, 8, 10 9, 12, 15 12, 16, 20 15, 20, 25 * What’s the pattern within and between the lines of Pythagorean Theorem Triples above? * What are the next 3 Triples in this pattern? 18, 24, 30

Pythagorean Theorem – Prove It! Converse of Pythagorean Theorem 1.) Is a triangle with side measures of 30, 40, and 50 units a right triangle? Prove it! 2.) Is a triangle with side measures of 6, 7, and 12 units a right triangle? Prove it!