# How do you identify a Pythagorean triple?

**Determine**if the following lengths are

**Pythagorean Triples**. Plug the given numbers into the

**Pythagorean**Theorem. Yes, 7, 24, 25 is a

**Pythagorean Triple**and sides of a right triangle. Plug the given numbers into the

**Pythagorean**Theorem.

A.

### How many Pythagorean triples are there?

So we can make infinitely many triples just using the (3,

**4**,**5**) triple. Euclid's Proof that there are Infinitely Many Pythagorean Triples.#### What are two Pythagorean triples?

The square of the length of the hypotenuse of a right triangle is the sum of the squares of the lengths of the**two**sides. This is usually expressed as a+b^{2}= c^{2}. Integer^{2}**triples**which satisfy this equation are**Pythagorean triples**. The most well known examples are (3,4,5) and (5,12,13).#### What is the Pythagorean triples?

A**Pythagorean triple**consists of three positive integers a, b, and c, such that a^{2}+ b^{2}= c^{2}. If (a, b, c) is a**Pythagorean triple**, then so is (ka, kb, kc) for any positive integer k. A primitive**Pythagorean triple**is one in which a, b and c are coprime (that is, they have no common divisor larger than 1).#### Who was Pythagoras?

**Pythagoras**, (born c. 570 bce, Samos, Ionia [Greece]—died c. 500–490 bce, Metapontum, Lucanium [Italy]), Greek philosopher, mathematician, and founder of the**Pythagorean**brotherhood that, although religious in nature, formulated principles that influenced the thought of Plato and Aristotle and contributed to the

Updated: 2nd October 2019