pythagorean theorem – prove it! converse of pythagorean theorem 1.) is a triangle with side...

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 302 + 402 = 502 (900 + 1600 = 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 62 + 72 ≠ 122 (36 + 49 ≠ 144).

Pythagorean TriplesA Pythagorean Triple is a set of positive integers, a, b, and c, that fit the rule:

a2 + b2 = c2.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 TriplesGenerating 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 TriplesFollow 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:74924 & 257, 24, 25

Example:1112160 & 6111, 60, 61

Pythagorean Triples

Other easy to remember Pythagorean Triples are:

3, 4, 56, 8, 109, 12, 1512, 16, 2015, 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!