Special Triangles

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Special Triangles
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EXAMPLE 1
Find the length of the hypotenuse.
SOLUTION
Substitute.
11.31
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EXAMPLE 1
EXAMPLE 1
Find the length of the hypotenuse.
Substitute.
Product of square roots
6
Simplify.
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EXAMPLE 2
Find the lengths of the legs in the triangle.
SOLUTION
Substitute.
5 x
Simplify.
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EXAMPLE 3
Standardized Test Practice
SOLUTION
o
o
45-45-90 Triangle Theorem
Substitute.
6
for Examples 1,2 and 3
GUIDED PRACTICE
Find the value of the variable.
1.
SOLUTION
Substitute.
2 x
Simplify.
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for Examples 1,2 and 3
GUIDED PRACTICE
Find the value of the variable.
2.
SOLUTION
Substitute.
y 2
Simplify.
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for Examples 1,2 and 3
for Examples 1,2 and 3
GUIDED PRACTICE
GUIDED PRACTICE
Find the value of the variable.
3.
SOLUTION
Substitute.
Simplify.
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for Examples 1,2 and 3
for Examples 1,2 and 3
GUIDED PRACTICE
GUIDED PRACTICE
4. Find the leg length of a 45-45-90 triangle
with a hypotenuse length of 6.
SOLUTION
Substitute.
6/v2 leg
Simplify.
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Hypotenuse Leg v2
Independent Practice
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Another Type of Special Right Triangle
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EXAMPLE 1 and 2
Example 4
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Example 4
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Example 4 Independent Practice
6. x 21, 7. x 10 and 8. x 62
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Example 5
EXAMPLE 5
Find the values of x and y. Write your answer in
simplest radical form.
STEP 1
Find the value of x.
Multiply fractions.
Simplify.
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Example 5
EXAMPLE 5
STEP 2
Find the value of y.
Substitute and simplify.
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EXAMPLE 6
Find a height
Mixed Types
Dump Truck
SOLUTION
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EXAMPLE 6
Find a height
Mixed Types
Triangle Theorem
Use a calculator to approximate.
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EXAMPLE 6
Find a height
Mixed Types
Substitute.
7 s
Divide each side by 2.
Substitute.
Use a calculator to approximate.
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for Examples 4, 5 and 6
GUIDED PRACTICE
Mixed Types
Find the value of the variable.
SOLUTION
Substitute.
Simplify.
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What happens if you start with an equilateral
triangle?
for Examples 4, 5 and 6
GUIDED PRACTICE
Find the value of the variable.
SOLUTION
All side are equal, therefore it is an
equilateral triangle a 30 - 60 - 90 triangle
can be found by dividing an equilateral triangle
in half
longer leg 2 shorter leg
Substitute.
Simplify.
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Keep Practicing!