The Pythagorean Theorem

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The Pythagorean Theorem

• By
• Melissa Selby

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Review Parts of a triangle
Hypotenuse- The longest side of a triangle.
Hypotenuse
Legs
Legs The two shortest sides of a triangle.
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Pythagorean Theorem

• The square of the hypotenuse is equal to the
  squares of the legs of the triangle.
• Used only on right triangles.

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Formulain terms of variables
ABC
C
A
B
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Examples
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A2, B2.5, C?

• Lets label the parts.

C?
A 2
B 2.5
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Original formula ABC
C?
A 2
B 2.5
22.5C 46.25C 46.2510.25 10.25C
ñ10.25ñC 3.20 C
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Common Mistakes

• When you get to the end of your problem and you
  have something like
• 125C
• Do not forget to take the square root of both
  sides

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Common Mistakes

• Always round to the nearest hundredth
• 1.25576188999 1.26

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Common Mistakes

• vs.
• When you round use
• not
• Why?

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Other ways to write the Pythagorean Theorem

• B²C²-A²
• And
• A²C²-B²

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How did we get them?

• Original A²B²C²
• Subtract A from both sides
• -A²A²B²C²-A²
• New formula! B²C²-A²

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How did we get them?

• Original A²B²C²
• Subtract B from both sides
• -B²A²B²C²-B²
• New formula! A²C²-B²

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Lets make them harder!
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A3 B? C5

• Which version of the Pythagorean theorem should
  we use?
• 1.) A²B²C²
• 2.) B²C²-A²
• 3.) A²C²-B²
• 2.) B²C²-A²

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A3 B? C5

• Label the parts

C5
A3
B?
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B²5²-3²

• B²25-9
• B²16
• vB² v 16
• B4

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A? B8 C10

• Which version of the Pythagorean theorem should
  we use?
• 1.) A²B²C²
• 2.) B²C²-A²
• 3.) A²C²-B²
• 3.) A²C²-B²

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A? B8 C10

• Label the parts

C10
A?
B8
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A²10²-8²

• A²10²-8²
• A²100-64
• A²36
• vA² v 36
• A6

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Word Problem!!!
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The story of
Rapunzel and Her Prince
My way
Rapunzel
Prince Charming
Castle
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Rapunzel and her prince charming have a new
problem.Rapunzel cut her hair! Now Prince
Charming cant reach her.What is he going to
do!?!
It will be o.k. sweetheart. Ill figure it out
Oh no!
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Well, lucky for Rapunzel her Prince Charming is a
rich engineer.Prince charming knows he just
needs the measurements of the building and his
ladder.Can you help him find the height of the
castle?
Each line is one hundred feet
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Now we need to know how long Prince Charmings
ladder is.
Each step is one hundred and ten feet from the
last one.
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What do we want to know?
How far from the bottom of the castle does Prince
Charming need to put his ladder?
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What do we know?

• The ladder is 1,210 feet from the ground to the
  top step.
• The castle is 1,000 feet tall

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Lets make it a right triangle.
Cladder
Acastle
B?
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Put it in a formula.

• B²C²-A²
• A1000 B? C1210
• B²1210²-1000²
• B²1464100-1000000
• B²464100
• v B² v 464100
• B681.24885
• round
• B681.25

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So, how far from the bottom of the castle does
prince charming need to put his ladder?
681.25 Feet
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Review
Do the work on your paper
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A16 B12 C?

• 35
• 64
• 22
• 20
• Dont cheat!

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Sorry that is incorrectLets work through the
problem

• 16²12²C²
• 256144C²
• v 400 v C²
• 20C

Try again
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Correct!Go to the next problem
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A? B15 C32

• 30.33
• 28.27
• 29.25
• 55.55

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Sorry that is incorrectLets work through the
problem

• 32²-15²A²
• 1024-225A²
• v299vA²
• 28.27A

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Correct!
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The end