Transcript Pythagoras Theorem

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
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QR2 = QP2 + PR2
QR2 = 42 + 72
QR2 = 16 + 49
QR2 = 65
QR = √65
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?
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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
50 mm
15 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
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