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Understanding 45-45-90 Triangles: Theorem and Examples

This guide covers the properties of 45-45-90 triangles, emphasizing the relationship between the legs and the hypotenuse. In a 45-45-90 triangle, both legs (x) are congruent, and the hypotenuse (c) can be calculated as c = x√2. Two examples demonstrate how to find the missing sides: Example #1 involves calculating the hypotenuse when the leg length is 5, and Example #2 requires rationalizing the hypotenuse from a leg length of 12. For additional practice, refer to the assignments on page 153 of your textbook.

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Understanding 45-45-90 Triangles: Theorem and Examples

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  1. Math 2Y 45°-45°-90° Triangles

  2. 45-45-90 Δ Theorem • In a 45-45-90 Δ: hypotenuse = leg = x 45o __ x __ 45o __ __ x

  3. Example #1: Find c Remember to label your drawing with x, x and x√2!! 5 x = c = x√2 c = 5√2 __ 45° __ 5 = x

  4. Example #2: Find f. __ __ f Rationalize! x = x 45° 12 = x√2 f = 6√2

  5. Assignment Use your textbook… pg. 153: #1-12 #14, 16, 18, 20, 22 (Be sure to copy the picture and label your sides!)

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