Miss Giraulo

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Pythagorean Theorem

• Miss Giraulo

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Pythagorean Theorem

• Pythagoras was a great Mathematician who was the
  first to create the music scale of today. He also
  created theorems. One of his most famous theorem
  was a2b2c2

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Review of the Necessary Basic Concepts

• You may be familiar with some of the concepts
  presented in the next few slides, allowing us to
  go through them very quickly. However, I hope
  that you will find some interesting concepts.

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Naming the Sides

• The letters a, b, and c are normally used to
  refer to the three sides of a triangle.

Side a and b are called legs.
a Leg
c
Angel C The angel opposite the right triangle is
called the hypotenuse
B leg
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• The letter a stands for altitude and b for base.
• The c is typically used for the third side,
  called the hypotenuse.
• Both sides a and b can be switched
• The hypotenuse is always the longest side.

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Did You understand?
Which sides of the right triangle are the legs?
Side a and b are the legs of the right triangle.
c
a

Which side of the right triangle is the
hypotenuse ?
Side c is the hypotenuse of the right triangle.
b
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The formula

• We can use this formula to determine the lengths
  of any side in right triangle if you we are given
  the other two sides.

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9 in
20 in
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12 in
18 in
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The Formula

• Leg2 Leg2 hypotenuse2
• A2 b2 c2

92 122 C2 81 144 C2 225 C2 v225
vc 15 c
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9 in
12 in
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You can also use this formulafind side a or b.
a2 b2 c2 182 b2 302 424 b2 900 -424
-424 b2 524 vb v524 b 24

30 in
18 in
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Lets Try A Few More
a2 b2 c2 32 42 C2 9 16 c2 25 c2 v25
vc 5 c
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3in
4 in
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Try these with a partner.
a2 b2 c2 62 122 C2 36 144 c2 169 c2
v169 vc 13 c

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12
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Try This One On Your Own.
a2 b2 c2 62 82 C2 36 64 c2 100 c2
v100 vc 10 c
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6in
8in
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Your Task

• You and your partner are going to use graph paper
  and a ruler and draw 3 right triangles.
• After you draw the triangles you are going test
  the theory.

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Your Task

•  Using excel you are going to create a chart that
  records the sides of each of your triangles.

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Excel
Did you know that........

• There is a function on Excel that will
  automatically find the 3rd side of a right
  triangle when given the other 2 sides
• Take a few minutes and experiment with your
  partner and see if you can find it.
• The computer does not have this theorem but it
  has a function that we use in the theorem.

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Find it yet?

• What is the first step?
• squaring the sides
• A2 b2 c2
• 32 42 c2
• Hint
• (3x3) (4x4)

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3
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Find it yet?

• HINT
• The last step in this formula is finding the
  square root.
• The function name is SQRT.
• Remember In order for this formula to work we
  have to tell the computer which cells to find
  the square root of.

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Steps
A B
C D

1 2 3
To find the Side C of triangle one Function-
SQRT In the number box type ( B2B2 C2C2) 5
will appear in D3
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Try Some
Find side C on Excel
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Good Job
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Homework

• Prove Pythagorean Theorem
• Find an object in your house that is a right
  triangle and measure it. Use the formula
• to test it.