Is a 45-45-90 Triangle a Pythagorean Triple?

Explore whether a 45-45-90 triangle qualifies as a Pythagorean triple. Learn the key definitions and concepts in geometry.

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A 45-45-90 triangle is not a Pythagorean triple. Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the equation a^2 + b^2 = c^2. In a 45-45-90 triangle, the sides follow the ratio 1:1:√2, which does not meet the integer criterion required for Pythagorean triples.

FAQs & Answers

  1. What is a Pythagorean triple? A Pythagorean triple is a set of three positive integers (a, b, c) such that a² + b² = c².
  2. What are the side ratios of a 45-45-90 triangle? In a 45-45-90 triangle, the sides have a ratio of 1:1:√2.
  3. How do you determine if a triangle is a Pythagorean triple? To determine if a triangle is a Pythagorean triple, check if the integers satisfy the equation a² + b² = c².
  4. Why is a 45-45-90 triangle not a Pythagorean triple? A 45-45-90 triangle does not meet the integer requirement of Pythagorean triples due to its sides being in irrational ratios.

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Interested in more geometry content? Check out our videos on triangle types and the Pythagorean theorem for a deeper understanding of fundamental mathematical principles.

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