What Is the 45-45-90 Triangle Rule in Geometry?

Learn the 45-45-90 triangle rule: equal legs and hypotenuse as leg × √2 for easy geometric problem solving.

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The 45-45-90 triangle rule states that in this special right triangle, the legs are of equal length, and the hypotenuse is the leg length multiplied by the square root of 2. This means if each leg is of length 'a,' then the hypotenuse will be 'a√2.' This rule is valuable for quickly solving geometric problems involving this specific type of triangle.

FAQs & Answers

  1. What are the side lengths in a 45-45-90 triangle? In a 45-45-90 triangle, both legs are equal in length, and the hypotenuse is the leg length multiplied by the square root of 2.
  2. How do you calculate the hypotenuse in a 45-45-90 triangle? Multiply the length of either leg by √2 to find the hypotenuse in a 45-45-90 triangle.
  3. Why is the 45-45-90 triangle rule useful in geometry? It allows for quick computation of side lengths in right triangles with equal legs, helping to solve problems efficiently.
  4. What makes the 45-45-90 triangle a special right triangle? It has two equal legs and a hypotenuse determined by a specific ratio, simplifying calculations compared to arbitrary triangles.

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