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Intermediate △ Geometry Topic 16 of 100

Pythagorean Triples

Integer right triangles such as 3-4-5 and 5-12-13.

Key idea

Integer right triangles such as 3-4-5 and 5-12-13.

In depth

A Pythagorean triple is a set of whole numbers (a, b, c) with a² + b² = c², such as 3-4-5, 5-12-13, 8-15-17. Multiples of triples also work. Euclid’s formula m² − n², 2mn, m² + n² generates them.

Worked example

With m = 2, n = 1: 3, 4, 5. With m = 3, n = 2: 5, 12, 13.

Real-world uses

Common mistake

Assuming every set of three consecutive numbers works. Only 3, 4, 5 does.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Pythagorean Triples?

Integer right triangles such as 3-4-5 and 5-12-13. It is a topic at the intermediate level in Geometry.

Where is Pythagorean Triples used in real life?

Real-world examples: Setting out right angles on a building site with a 3-4-5 rope; Quick mental checks for right triangles.

What should I learn before Pythagorean Triples?

Make sure you are comfortable with Pythagorean Theorem, the previous topic in Geometry.

What is a common mistake with Pythagorean Triples?

Assuming every set of three consecutive numbers works. Only 3, 4, 5 does.

How can I practise Pythagorean Triples?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Pythagorean Triples?

Move on to Special Right Triangles next.

Related intermediate topics in Geometry