The Theorem of Pythagoras

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The Theorem of Pythagoras
How to label and name a right angled triangle.
The 900 angle is the largest angle.
The largest side is opposite the largest angle.
The largest side is called the HYPOTENUSE.
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The Theorem of Pythagoras
Capital letters are used for angles.
The sides opposite the angles are given lower
case letters.
B
a
C
A
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The Theorem of Pythagoras
Capital letters are used for angles.
The sides opposite the angles are given lower
case letters.
B
a
C
b
A
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The Theorem of Pythagoras
Capital letters are used for angles.
The sides opposite the angles are given lower
case letters.
B
a
c
C
b
A
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The Theorem of Pythagoras
Capital letters are used for angles.
The sides opposite the angles are given lower
case letters.
B
a
c
C
b
A
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The Theorem of Pythagoras
Draw to scale the right angled triangle shown
below.
Measure the length of side a. What do you get?
a cm
3 cm
5 cm.
4 cm
Measure the length of side b. What do you get?
b cm
9 cm
15 cm
12 cm
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Born about 569 BC in Samos, IoniaDied about
475 BC                              
It was Pythagoras who discovered the link between
the lengths of the sides in a right angled
triangle.
Because of this the formula carries his name.
The formula is known as the Theorem of
Pythagoras.
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a
c
b
Always START with the hypotenuse
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r
t
s
10
v
x
w
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b
a
c
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In a right angled triangle, the square of the
hypotenuse is equal to the sum of the squares of
the other two sides.
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Page 71 Exercise 2A
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3. Calculate x in the diagram below.
There are no right angled triangles.
13 cm
We need to make one.
10 cm
13 cm
5 cm
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Page 72 Exercise 2B
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Calculating distance using coordinates
How do we calculate the length of the line?
Lets make a right angled triangle.
Now we can measure the horizontal and vertical
distance.
We can now use the theorem of Pythagoras to
calculate the distance between the two points.
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3
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Page 75 Exercise 4A
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The Converse of the Theorem of Pythagoras
The theorem
In a right angled triangle, the square of the
hypotenuse is equal to the sum of the squares of
the other two sides.
The converse
If in a triangle, the square of the largest side
is equal to the sum of the squares of the other
two sides, then the triangle is right angled.
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Longest side
Shorter sides
Hence the triangle is right angled by the
converse of Pythagoras.
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Page 79 Exercise 5A