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Geometry Notes

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Dive into the world of special right triangles with a focus on 45-45-90 triangles. This lesson covers essential properties, relationships, and techniques to effectively solve problems involving special right triangles. Learn to identify legs and hypotenuse, understand congruence, and utilize methods for finding all sides and angles. Through examples and practice problems, you will gain a solid grasp of how to apply special right triangle relationships, including rationalizing the denominator in various calculations. Perfect for enhancing your geometry skills!

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Geometry Notes

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  1. Geometry Notes Lesson 5.2A Special Right Triangles 45/45/90 T.2.G.5 Use the special right triangle relationships (30˚-60˚-90˚ and 45˚-45˚-90˚) to solve problems

  2. 45° 45° 45°-45°-90° Special Right Triangle • Label the sides of the triangle: leg leg hypotenuse

  3. 45° 45° 45°-45°-90° Special Right Triangle • Examples and Patterns:

  4. 45°-45°-90° Special Right Triangle • On a 45°-45°-90° triangle, the following are always true: • The legs are always • Hypotenuse = • Leg = congruent

  5. Steps to Finding all Sides and Angles in a 45-45-90 Triangle: Ask yourself: a) Am I getting bigger or smaller? b) Should I multiply or divide by ? c) If dividing, remember to rationalize the denominator!

  6. a c 6 Example 1: • Find the value of the missing variable:

  7. b a Example 2: • Find the value of the missing sides:

  8. a b 6 Example 3: • Find the value of the missing sides:

  9. 3 You try these: • Find the missing sides.

  10. 9 You try these: 2.

  11. 4 You try these: 3.

  12. Rationalizing Denominator of • If Even number: If Odd number:

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