What Is the 45-45-90 Triangle Theorem and How Does It Work?

Learn the 45-45-90 triangle theorem: equal legs and a hypotenuse equal to leg × √2 in these special right triangles.

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The 45°-45°-90° triangle theorem states that in a right triangle where the two non-hypotenuse angles are 45°, the lengths of the legs are equal, and the length of the hypotenuse is the leg length multiplied by the square root of 2. This theorem simplifies the calculation of side lengths in these specific triangles.

FAQs & Answers

  1. What are the side ratios in a 45-45-90 triangle? In a 45-45-90 triangle, the legs are equal in length, and the hypotenuse is the length of a leg multiplied by the square root of 2.
  2. How do you calculate the hypotenuse in a 45-45-90 triangle? Multiply the length of one leg by √2 to find the hypotenuse length in a 45-45-90 triangle.
  3. Why is the 45-45-90 triangle important in geometry? The 45-45-90 triangle theorem simplifies calculations in right triangles where the two non-right angles are equal, making it a fundamental concept in geometry.

Watch More

For a deeper understanding of special right triangles, explore our related videos and articles on the 30-60-90 triangle theorem and practical examples using these essential geometry principles.

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