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The Pythagorean Theorem

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Pythagorean Theorem ... to write the Pythagorean Theorem. B =C -A . And ... Which version of the Pythagorean theorem should we use? 1.) A B =C . 2.) B =C -A ... – PowerPoint PPT presentation

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Title: The Pythagorean Theorem


1
The Pythagorean Theorem
  • By
  • Melissa Selby

2
Review Parts of a triangle
Hypotenuse- The longest side of a triangle.
Hypotenuse
Legs
Legs The two shortest sides of a triangle.
3
Pythagorean Theorem
  • The square of the hypotenuse is equal to the
    squares of the legs of the triangle.
  • Used only on right triangles.

4
Formulain terms of variables
ABC
C
A
B
5
Examples
6
A2, B2.5, C?
  • Lets label the parts.

C?
A 2
B 2.5
7
Original formula ABC
C?
A 2
B 2.5
22.5C 46.25C 46.2510.25 10.25C
ñ10.25ñC 3.20 C
8
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

9
Common Mistakes
  • Always round to the nearest hundredth
  • 1.25576188999 1.26

10
Common Mistakes
  • vs.
  • When you round use
  • not
  • Why?

11
Other ways to write the Pythagorean Theorem
  • B²C²-A²
  • And
  • A²C²-B²

12
How did we get them?
  • Original A²B²C²
  • Subtract A from both sides
  • -A²A²B²C²-A²
  • New formula! B²C²-A²

13
How did we get them?
  • Original A²B²C²
  • Subtract B from both sides
  • -B²A²B²C²-B²
  • New formula! A²C²-B²

14
Lets make them harder!
15
A3 B? C5
  • Which version of the Pythagorean theorem should
    we use?
  • 1.) A²B²C²
  • 2.) B²C²-A²
  • 3.) A²C²-B²
  • 2.) B²C²-A²

16
A3 B? C5
  • Label the parts

C5
A3
B?
17
B²5²-3²
  • B²25-9
  • B²16
  • vB² v 16
  • B4

18
A? B8 C10
  • Which version of the Pythagorean theorem should
    we use?
  • 1.) A²B²C²
  • 2.) B²C²-A²
  • 3.) A²C²-B²
  • 3.) A²C²-B²

19
A? B8 C10
  • Label the parts

C10
A?
B8
20
A²10²-8²
  • A²10²-8²
  • A²100-64
  • A²36
  • vA² v 36
  • A6

21
Word Problem!!!
22
The story of
Rapunzel and Her Prince
My way
Rapunzel
Prince Charming
Castle
23
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!
24
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
25
Now we need to know how long Prince Charmings
ladder is.
Each step is one hundred and ten feet from the
last one.
26
What do we want to know?
How far from the bottom of the castle does Prince
Charming need to put his ladder?
27
What do we know?
  • The ladder is 1,210 feet from the ground to the
    top step.
  • The castle is 1,000 feet tall

28
Lets make it a right triangle.
Cladder
Acastle
B?
29
Put it in a formula.
  • B²C²-A²
  • A1000 B? C1210
  • B²1210²-1000²
  • B²1464100-1000000
  • B²464100
  • v B² v 464100
  • B681.24885
  • round
  • B681.25

30
So, how far from the bottom of the castle does
prince charming need to put his ladder?
681.25 Feet
31
Review
Do the work on your paper
32
A16 B12 C?
  • 35
  • 64
  • 22
  • 20
  • Dont cheat!

33
Sorry that is incorrectLets work through the
problem
  • 16²12²C²
  • 256144C²
  • v 400 v C²
  • 20C

Try again
34
Correct!Go to the next problem
35
A? B15 C32
  • 30.33
  • 28.27
  • 29.25
  • 55.55

36
Sorry that is incorrectLets work through the
problem
  • 32²-15²A²
  • 1024-225A²
  • v299vA²
  • 28.27A

37
Correct!
38
The end
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