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Special Right Triangles (45-45-90 & 30-60-90)

Special Right Triangles (45-45-90 & 30-60-90). 9.3.3.5 Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results. Guiding Question: What is the relationship between the sides of special right triangles?.

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Special Right Triangles (45-45-90 & 30-60-90)

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  1. Special Right Triangles (45-45-90 & 30-60-90) 9.3.3.5 Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.

  2. Guiding Question: What is the relationship between the sides of special right triangles? • 2 types of special right triangles. • 1. 45 – 45 - 90 triangle • 2. 30 – 60 – 90 triangle • Lesson Objectives: I will be able to use the ratios of special triangles to find missing sides.

  3. Guiding Question: What is the relationship between the sides of special right triangles? • 45 – 45 – 90 Special Rt. Triangles • The sides follow this ratio: 1 : 1 : • If the leg length is 5, then the hypotenuse would be 5. So the side ratios would be . • What if the leg length is equal to ?

  4. Guiding Question: What is the relationship between the sides of special right triangles? 1. What if the hypotenuse is 2. What if the hypotenuse is equal to 3. What if the hypotenuse is equal to 4? 4. What if a leg is equal to 6?

  5. Guiding Question: What is the relationship between the sides of special right triangles? • In a 30 – 60 – 90 right triangle the sides have the ratio of . • If the shortest side equals 3, what do the other 2 sides equal? • If the middle side of a triangle is , what are the other 2 sides?

  6. Guiding Question: What is the relationship between the sides of special right triangles? What are the side lengths of a 30-60-90 triangle if the long side is 12? What if the middle side length is equal to 6? 3. What if the shortest side is equal to ?

  7. Assignment: Special Rt. Triangle worksheet.

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