Special Triangles

1
Special Triangles

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45 45 90 Triangle 30 60 90
Triangle
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45 45 90 Triangle
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Consider a square with sides X.
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If we draw in diagonal well obtain two
triangles.
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6
Take a closer look at the triangle ABC, its a
Right Triangle!
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7
Applying the Pythagorean Theorem, we obtain the
length of our diagonal .
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This is fundamental yet powerful result.
8
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9
Example 1)
becomes
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Example 2)
becomes
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11
Example 3)
becomes
Why? See next page
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12
Using the 45- 45- 90 relationship. . .
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13
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30 60 90 Triangle
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15
Consider an equilateral triangle.
We know equilateral triangles have 1.
Interior angles each measuring 60. 2. All
three sides have equal length.
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16
Bisecting angle ACB by drawing a line segment
from vertex C to point D on side , we obtain
the following
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Now, represent the lengths of our equilateral
triangle by 2X.
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Weve created a 30-60-90 triangle.
We need to determine the length of one of our
legs, its represented by the ?
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19
Using the Pythagorean Theorem,
We can now apply this result.
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20
Example 1)
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21
Example 2)
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Using,
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Example 3)
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Using,
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