The Theorem Of Pythagoras

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The Theorem Of Pythagoras

• Pythagoras was a Greek Mathematician.(580-500B.C).
  2500 years old is even older than your teacher.
• He was eccentric. (mad!!) Dont mention v 2 to
  him!!
• He discovered an amazing rule about right angled
  triangles.

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HUH????
Pythagoras Theorem says The square on the
longest side of the triangle is equal to the sum
of the squares on the other two sides.
3
What does it all mean?
Draw squares on the three sides of the triangle.
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The area of the smaller squares adds up to the
area of the largest square.


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Pythagoras Theorem
c2
c
b2
b
a
This is called Pythagoras Theorem.
c2a2b2
a2
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Does this work for all right-angled triangles?
a b c a2 b2 c2
3 4
5 12
6 8
8 15
5
9
16
25
c
a
13
25
144
169
36
64
100
10
b
64
225
289
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By considering all the numbers in the completed
table you can see what Pythagoras discovered.
The Theorem Of Pythagoras a2 b2 c2 This
works for ALL right-angled triangles.
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Calculating An Unknown Side.

• The longest side of a right angled triangle is
  called the hypotenuse.

a
c

• Pythagoras discovered that the sum of the squares
  of the two shorter sides is equal to the square
  of the hypotenuse.

HYPOTENUSE
b
c2a2b2
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Find the side C (the hypotenuse) in this
triangle.
c
6 (b)
8 (a)
Hint Follow this routine exactly every time, to
solve Pythagoras problems easily.
Solution.
c2 a2 b2
c2 82 62
c2 64 36
c2 100
c v
100
c 10
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Find the unknown side in each of the triangles
below.
12.04
9.22
10.73
24.7
24.38