Pythagorean theorem

1
Pythagorean theorem

• 6.1

2
Definitions

• Right triangle has one right angle
• Hypotenuse- the side opposite the right angle
  which is the longest side
• Legs of a right triangle- the other two sides

Leg
Hypotenuse
Leg
3
Objective- To solve problems involving the
Pythagorean Theorem.
For Right Triangles Only!
hypotenuse
- always opposite the right angle
leg
leg
4
Objective- To solve problems involving the
Pythagorean Theorem.
For Right Triangles Only!
hypotenuse
c
a
leg
b
leg
5
Objective- To solve problems involving the
Pythagorean Theorem.
For Right Triangles Only!
Pythagorean Theorem
c
a
b
6
Solve for x.
x
6
8
7
Solve for y.
7
4
y
8
Solve for t.
6
t
15
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Pythagorean Triples
3 4 5
6 8 10
9 12 15
12 16 20
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Pythagorean Triples
3 4 5
5 12 13
7 24 25
6 8 10
10 24 26
14 48 50
9 12 15
15 36 39
21 72 75
12 16 20
12
9
15
11
A car drives 20 miles due east and then 45
miles due south. To the nearest hundredth of a
mile, how far is the car from its starting point?
20 miles
x
45 miles
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Converse of the Pythagorean Theorem

• If the square of the length of one side is equal
  to the squares of the lengths of the other two
  sides then the triangle is right.
• Length 5
• Length 13
• Length 12 ..Is this a right triangle?
• How about 24,7 and 25?

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Squares and Square Roots

• Square root one of two equal factors of a
  number
• Perfect Sq.- number that is the square of an
  integer
• Perfect Square 9 is a perfect square because
  3(3) 9
• The number 3 is a sq. root because 32 9
• is called a radical sign and indicates the
  positive sq root of a number. All positive
  numbers have 2 sq. roots. Negative numbers do NOT
  have sq. roots

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Homework

• Pythagorean Packet