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Pythagorean Triples

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Pythagorean Triples

Study Guide

Key Definition

A Pythagorean triple consists of three positive integers $(a, b, c)$ such that $a^2 + b^2 = c^2$.

Important Notes

A Pythagorean triple is in the form $(a, b, c)$ where $a < b < c$
Common triples include $(3, 4, 5)$ and $(5, 12, 13)$
Use the Pythagorean theorem to verify triples
Not all integer sets are Pythagorean triples
Memorize common triples for quick recall

Mathematical Notation

$a^2$ means a squared

$+$ represents addition

$=$ signifies equality

$\sqrt{x}$ represents the square root of x

$(a, b, c)$ represents a triple

Remember to use proper notation when solving problems

Why It Works

The Pythagorean theorem $a^2 + b^2 = c^2$ holds true for right triangles, allowing the verification of integer triples.

Remember

Pythagorean triples are specific sets of integers that satisfy $a^2 + b^2 = c^2$.

Quick Reference

Common Triple:$(3, 4, 5)$

Verification Formula:$a^2 + b^2 = c^2$

Understanding Pythagorean Triples

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A Pythagorean triple is a set of three positive integers $(a, b, c)$ where $a^2 + b^2 = c^2$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is a Pythagorean triple?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You need to verify if a ladder of length 10 meters and base 6 meters reaches the top of a wall of height 8 meters. Use the Pythagorean theorem to check.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine if the set $(7, 24, 25)$ is a Pythagorean triple.

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following is NOT a Pythagorean triple?

Recap

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Review key concepts and takeaways