7.1 Apply the Pythagorean theorem.

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7.1 Apply the Pythagorean theorem.
Theorem 7.1 Pythagorean Theorem In a right
triangle, the square of the length of the
hypotenuse is equal to the sum of the squares of
the lengths or the legs.
c
a
c2a2b2
b
2
EXAMPLE 1
Find the length of a hypotenuse
SOLUTION
Pythagorean Theorem
x2 62 82
Substitute.
x2 36 64
Multiply.
x2 100
Add.
x 10
Find the positive square root.
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for Example 1
GUIDED PRACTICE
1.
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for Example 1
GUIDED PRACTICE
2.
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EXAMPLE 2
Standardized Test Practice
SOLUTION
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EXAMPLE 2
Standardized Test Practice
SOLUTION
162 42 x2
Substitute.
256 16 x2
Multiply.
240 x2
Subtract 16 from each side.
Find positive square root.
15.492 x
Approximate with a calculator.
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for Example 2
GUIDED PRACTICE
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for Example 2
GUIDED PRACTICE
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EXAMPLE 3
Find the area of an isosceles triangle
Find the area of the isosceles triangle with side
lengths 10 meters, 13 meters, and 13 meters.
SOLUTION
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EXAMPLE 3
Find the area of an isosceles triangle
c2 a2 b2
Pythagorean Theorem
132 52 h2
Substitute.
169 25 h2
Multiply.
144 h2
Subtract 25 from each side.
12 h
Find the positive square root.
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EXAMPLE 3
Find the area of an isosceles triangle
STEP 3
Find the area.
Area
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for Example 3
GUIDED PRACTICE
5.
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for Example 3
GUIDED PRACTICE
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Pythagorean Triple a set of three positive
integers a, b, and c that satisfy the equation
c2a2b2
You may find it helpful to memorize the basic
Pythagorean triples, shown in bold, for
standardized tests.
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EXAMPLE 4
Find the length of a hypotenuse using two methods
SOLUTION
Method 1 Use a Pythagorean triple.
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EXAMPLE 4
Find the length of a hypotenuse using two methods
SOLUTION
Method 2 Use the Pythagorean Theorem.
x2 102 242
Pythagorean Theorem
x2 100 576
Multiply.
x2 676
Add.
x 26
Find the positive square root.
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for Example 4
GUIDED PRACTICE
Find the unknown side length of the right
triangle using the Pythagorean Theorem. Then use
a Pythagorean triple.
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Daily Homework Quiz
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Daily Homework Quiz
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Daily Homework Quiz