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Slide 1:

Bell Ringer #85 Objective Be able to solve problems using special triangles

Lesson 66 • Special Right Triangles:

Lesson 66 • Special Right Triangles

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5.1 Special Right Triangles *You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90

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In a 45-45-90 triangle… LEGS ARE THE SAME LENGTH We will use a reference triangle to set up a proportion then solve.

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45-45-90 Right Triangle 1 1 This is our reference triangle for the 45-45-90.

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45-45-90 Right Triangle x x

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3 3 x 1 1 3 1 x EX: 1 Solve for x Let’s set up a proportion by using our reference triangle.

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5 5 x 1 1 5 1 x EX: 2 Solve for x

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x 3 1 1 x 1 3 45 EX: 3 Solve for x

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30-60-90

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30-60-90 Right Triangle 1 2 30 60 This is our reference triangle for the 30-60-90 triangle. We will use a reference triangle to set up a proportion then solve.

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30-60-90 Right Triangle x 2 x 30  60 

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60 30 x y 8 x 1 8 2 y 8 2 1 2 30 60 Ex: 1

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60 30 x 24 Solve for x 24 2 x 1 1 2 30 60 2x = 24 x = 12 Ex: 2

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60 30 x 14 14 2 x 1 1 2 30 60 2x = 14 x = 7 Ex: 3 y 14 2 y 30 60

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60 30 x x 1 1 2 30 60 x = 5 Ex: 4 y y 2 y = 10

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