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Special Right Triangles - Hypotenuse and Leg Relationships

Learn how to find the hypotenuse and leg lengths in special right triangles, including 45-45-90, equilateral, and 30-60-90 triangles. Discover the relationships between the sides and angles using multiplication, division, and square root operations.

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Special Right Triangles - Hypotenuse and Leg Relationships

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  1. 7.3 Special Right Triangles Chapter 7 Area

  2. Find the Hypotenuse, leave your answer in simplest radical form. 4 3 3 4 2 What do you notice? 2

  3. 45-45-90 Triangles (Isosceles Right Triangles) • The Legs are congruent • The Hypotenuse is the leg • times the √2 x√2 x x

  4. 45-45-90 Triangles (Isosceles Right Triangles) 5 5

  5. 45-45-90 Triangles If you are given the hypotenuse and Must find the leg, DIVIDE by √2 10√2

  6. 45-45-90 Triangles If you are given the hypotenuse and Must find the leg, DIVIDE by √2 20

  7. To Recap: 45-45-90 Triangles • Leg to Hypotenuse: Multiply by √2 • Hypotenuse to Leg: Divide by √2 • The Legs are always Congruent x√2 x x

  8. Equilateral Triangles • In an Equilateral Triangle, all sides and angles are congruent. Therefore, each angle is 60°. 60° 60° 60°

  9. Equilateral Triangles • If we cut it in half, what happens? Using Pythagorean Theorem, solve for the height of the triangle in simplest radical form. 30° 30° 10 10 5√3 60° 60° 5

  10. 30-60-90 Triangles • Long Leg is across from the 60° angle • Short Leg is across from the 30° angle • Hypotenuse is across from the right angle 30° Hypotenuse Long Leg 60° Short Leg

  11. 30-60-90 Triangles • Short Leg is always your starting point • Long Leg is √3 times the Short Leg • Hypotenuse is 2 times the Short Leg 30° Hypotenuse 2x Long Leg x√3 60° Short Leg x

  12. 30-60-90 Triangles • Short Leg to Hypotenuse: Multiply by 2 • Hypotenuse to Short Leg: Divide by 2 • Short Leg to Long Leg: Multiply by √3 • Long Leg to Short Leg: Divide by √3 30° Hypotenuse 2x Long Leg x√3 60° Short Leg x

  13. 30-60-90 Triangles 4 30° 60° 12 30° 60°

  14. 30-60-90 Triangles 30° 60° 6√3 15

  15. Practice

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