Pythagoras Theorem

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Pythagoras Theorem
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What is it?

• If you know two sides of a right angled triangle
  you can work out the other side.

This is the right angle
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How it works!

• 'The square on the hypotenuse is equal to the sum
  of the squares on the other two sides'

The hypotenuse is the longest side. It is always
opposite the right angle. Which side is the
hypotenuse in this diagram?
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How to find the hypotenuse

• The hypotenuse is a
• a2 b2 c2

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Worked Example

• QR2 QP2 PR2
• QR2 42 72
• QR2 16 49
• QR2 65
• QR v65
• QR 8.06 cm (this is the longest side so it
  should be bigger than the other two sides)

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Other types of questions
Is this triangle a right angled triangle?

• If it is then Pythagoras should work
• YZ should 10
• YZ2 52 92
• YZ2 25 81
• YZ2 106
• YZ 10.3 cm Is this triangle right angled?

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Other questions

• The farmer measured the red line to be 124metres.
  Is this field a perfect rectangle?

112m
50m
If it is then Pythagoras should work, because
there are two right angled triangles in a square
or rectangle. H2 502 1122 H2 2500
12,544 H2 15,044 H 122.7 m, Is this field a
perfect rectangle?
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Finding the smaller sides

• Instead of adding, you take the smaller number
  away from the bigger one
• YZ2 82 72
• YZ2 64 49
• YZ2 15
• YZ 3.9 cm

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Tricky Questions

• Find the sloping side of this rubber

35 mm
10 mm
10 mm
15 mm
50 mm
You have to find the right angled triangle and
the two sides you need H2 102 152 H2 100
225 H2 325 H 18.02 mm
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Pythagorean Triples

• These are three numbers that will fit into
  Pythagoras theorem e.g.
• 3, 4, 5
• 3² 4² 5²
• 9 16 25
• Are these numbers 6, 8, 9 Pythagorean triples?
• No, 100 does not equal 81