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Section 5.5 Special Right Triangles Note: Triangles in this section are always right triangles! 45-45-90 Triangles Theorem 1: In a triangle whose angles measure 0 45 , 0 45 , and 0 90 , the hypotenuse has a length equal to the product of 2 and the length of either leg. The ratio of the sides of a 45-45-90 triangle are: x : x : x 2 . 45-45-90 if this measure is given: and you want this measure: then do this: the leg hypotenuse multiply the leg by 2 hypotenuse the leg divide hypotenuse by 2 Note: The legs of a 45-45-90 are the same measure! 2 hypotenuse leg = hypotenuse = leg 2 30-60-90 Triangles Theorem 2: In a triangle whose angles measure 0 30 , 0 60 , and 0 90 , the hypotenuse has a length equal to twice the length of the shorter leg, and the length of the longer leg is the product of 3 And the length of the shorter leg. The ratio of the sides of a 30-60-90 triangle are: x : x 2:3 x .

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