Section 7

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Section 7 2 The Pythagorean theorem Its
converse

• Objectives
• To use the Pythagorean Theorem
• To use the Converse of the Pythagorean Theorem

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Pythagorean Theorem

•  

Used to find a missing side of a RIGHT triangle.
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Pythagorean Triple

• A set of nonzero whole numbers a, b, and c that
  satisfy the Pythagorean Theorem.

Common Pythagorean Triples 3, 4, 5 5, 12, 13
8, 15, 17 7, 24, 25
If you multiply each number in a Pythagorean
Triple by the same whole number, the three
numbers that result also form a Pythagorean Triple
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Example 1 Pythagorean Triples

• A) Find the length of the hypotenuse of ?ABC. Do
  the lengths of the sides of ?ABC form a
  Pythagorean Triple?

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• B) A right triangle has a hypotenuse of length 25
  and a leg of length 10. Find the length of the
  other leg. Do the lengths of the sides form a
  Pythagorean triple?

C) A right triangle has legs of length 16 and 30.
Find the length of the hypotenuse. Do the lengths
of the sides form a Pythagorean triple?
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Example 2 Using Simplest Radical Form

• A) Find the value of x. Leave your answer in
  simplest radical form.

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• B) The hypotenuse of a right triangle has length
  12. One leg has length 6. Find the length of the
  other leg. Leave your answer in simplest radical
  form.

C) Find the value of x. Leave your answer in
simplest radical form.
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Example 3 Real-World Connection

• A) The Parks Department rents paddle boats at
  docks near each entrance to the park. About how
  far is it to paddle from one dock to the other?

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• B) How far is home plate from second base on a
  baseball diamond?

C) How far is home plate from second base on a
softball diamond?
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Section 7 2 Continued

• Objectives
• To use the Converse of the Pythagorean Theorem

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Example 4 Finding Area

• A) Find the area of the triangle.

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• B) Find the area of the triangle.

C) The hypotenuse of an isosceles right triangle
has length 20 cm. Find the area.
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Converse of the Pythagorean Theorem

• If the square of the length of one side of a
  triangle is equal to the sum of the squares of
  the other two sides, then the triangle is a right
  triangle.

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Example 5 Is it a Right Triangle?

• Is each triangle a right triangle?
• A)

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B)
C) A triangle with side lengths 16, 48, and 50.
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Theorem 7 6

•  

Theorem 7 7
 
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Example 6 Classifying Triangles as Acute,
Obtuse, or Right.

• The lengths of the sides of a triangle are given.
  Classify each triangle as acute, obtuse, or
  right.
• 6, 11, 14
• 12, 13, 15
• 7, 8, 9

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Homework7 2 Ditto 1 19 Odds