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Simplifying Radical Expressions - Special Right Triangles

Learn to simplify radical expressions using the relationships among the sides in Special Right Triangles 45°-45°-90° and 30°-60°-90°. Understand the theorem that relates the lengths of the hypotenuse and legs.

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Simplifying Radical Expressions - Special Right Triangles

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  1. Do Now Simplify the radical expression. 1) = 2) = 3) =

  2. Geometry Objective: To use the relationships among the sides in Special Right Triangles 7.4: Special Right Triangles

  3. 45o, 45o, 90o Triangle Theorem • The length of the hypotenuse is times the length of the leg. 45o x 45o x

  4. 30o, 60o, 90o Triangle Theorem • The length of the hypotenuse is two times the length of the shorter leg and the length of the longer leg is times the length of the shorter leg. 60 2x x 30

  5. Examples Hypotenuse = times leg

  6. Examples (cont.)

  7. Examples (cont.) Hypotenuse is 2 times shorter side & the longer leg is times the shorter leg.

  8. Examples (cont.)

  9. Examples (cont.)

  10. Examples (cont.) 6

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