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**7-3 Special Right Triangles**

Goal 1: To use the properties of 45°-45°-90° triangles Find the measures of the missing sides. Leave answers in radical form.

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Solutions 1. 2 2. 3. 3

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**Right triangles whose angle measures are 45°-45°-90° or 30°-60°-90° **

are called special right triangles.

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The Triangle Start with a right isosceles triangle. This right isosceles triangle may be called a triangle. c x x To find the third, unknown side of the right triangle, use the Pythagorean Theorem. a2 + b2 = c2 Pythagorean Theorem x2 + x2 = c2 Substitution Property of Equality 2x2 = c2 Simplify = c Simplify

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**Theorem: In a 45-45-90 triangle, the hypotenuse is times as long as its leg.**

x x

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Triangles Multiply by Leg Hypotenuse Divide by

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**Ex. Find the values of the variable. 1. 2.**

x 3 x 3 x x

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Assignment: pp #1-11, 47-55

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