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**CHAPTER 8 RIGHT TRIANGLES**

8.4 SPECIAL RIGHT TRIANGLES

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**SPECIAL RIGHT TRIANGLES**

We will learn about 2 kinds of triangles that are well known in Geometry: 45° - 45° - 90° triangle, and 30° - 60° - 90° triangle. These triangles are identified by their angle measures and have sides with specific relationships.

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THEOREM 8-6 45° a√2 a a a 45° a a

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**EXAMPLES Find the value of x**

10√2 3√2 x 45° 10 x 45° 6

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**THEOREM 8-7 THEOREM 8-7 30° - 60° - 90° Theorem**

In a 30° - 60° - 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the short leg. 30° 2a a√3 60° a

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**EXAMPLE Find x and y. x = 18 x = 3√3 y = 9√3 y = 6√3 9 x x 9 30° 60° y**

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**PRACTICE Complete: If r = 6, t = _____ If s = 2√5, t = _____**

If t = √2, r = _____ If t = 10, s = _____ 6√2 2√10 1 5√2 t r 45° s

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**PRACTICE Complete: 8√3, 16 If q = 8, p = _____ and n = _____. 10, 10√3**

4, 8 3√3, 6√3 If q = 8, p = _____ and n = _____. If n = 20, q = _____ and p = _____. If p = 4√3, q = _____ and n = _____. If p = 9, q = _____ and n = _____. 30° n p q

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PRACTICE A diagonal of a square has length 6. What is the perimeter of the square? 12√2

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**CLASSWORK/HOMEWORK 8.4 Assignment Pg. 301, Classroom Exercises 1-12**

Pg , Written Exercises 2-28 even

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