Pythagorean Triples - Varsity Tutors

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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 tripleRemember 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

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Beginner Explanation

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

Practice Problems

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1

Quick Quiz

Single Choice QuizBeginner

Which of the following is a Pythagorean triple?

A$(3, 4, 5)$B$(2, 3, 5)$C$(5, 9, 11)$D$(6, 8, 15)$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

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.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

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

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Which of the following is NOT a Pythagorean triple?

A$(8, 15, 17)$B$(9, 10, 15)$C$(5, 12, 13)$D$(10, 24, 26)$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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