7.1-2 The Pythagorean Theorem

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7.1-2 The Pythagorean Theorem

• Mrs. Wilkins
• Geometry

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Objectives/Assignment

• Prove the Pythagorean Theorem
• Use the Pythagorean Theorem to solve real-life
  problems such as determining how far a ladder
  will reach.

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History Lesson

• Around the __ century BC, the Greek mathematician
  Pythagorus founded a school for the study of
  _____, mathematics and science. Many people
  believe that an early ___ of the Pythagorean
  Theorem came from this school.
• Today, the ___________ is one of the most famous
  theorems in geometry. Over ___ different proofs
  now exist.

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Theorem 9.4 Pythagorean Theorem

• In a _____ triangle, the square of the length of
  the hypotenuse is equal to the ___ of the squares
  of the legs.

a2 b2 c2
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Ex. 1 Finding the length of the hypotenuse.

• Find the value of x.

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Ex. 2 Finding the length of the leg.

• Find the value of x.

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Ex. 3 Finding the length of the leg.

• Find the value of x.

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Ex. 4 Finding the length of the hypotenuse.

• Find the value of x.

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Is the triangle acute, obtuse or right?
RIGHT ACUTE OBTUSE
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Ex. 5 Classify the triangles given their side
lengths

• 10, 11, 14
• 12, 16, 20
• 5, 6, 7

• 6, 8, 10
• 4, 7, 9
• 15, 36, 39

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7.1-2 The Pythagorean Theorem

• Mrs. Wilkins
• Geometry

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Find the unknown side length
18
x
12
13
Find the unknown side length
4
x
v5
14
Find the unknown side length
x
x
2v5
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Find the unknown side length
20
x
12
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Using the Pythagorean Theorem

• A Pythagorean triple is a set of _____ positive
  integers a, b, and c that satisfy the equation
  _________. For example, the integers 3, 4 and 5
  form a Pythagorean Triple because 32 42 52.

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Pythagorean Triples
3,4, 5 5, 12, 13 8, 15, 17 7, 24, 25
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The given lengths are two sides of a right
triangle. The sides together form a Pythagorean
triple. Find the length of the third side and
tell whether it is a leg or the hypotenuse.

• 24 and 51
• 20 and 25
• 72 and 75

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Pythagorean Triples
3,4, 5 5, 12, 13 8, 15, 17 7, 24, 25
6, 8, 10
15, 36, 39
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Classify the triangles given their side lengths
14, 25, 30
, 7, 10
,15, 16