Learn about the Pythagoras Theorem Apply the Pythagoras Theorem
to solve the triangles Students and Teachers will be able to
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Pythagoras was a Greek philosopher and religious leader. He was
responsible for many important developments in maths, astronomy,
and music.
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His students formed a secret society called the Pythagoreans.
As well as studying maths, they were a political and religious
organisation. Members could be identified by a five pointed star
they wore on their clothes.
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They had to follow some unusual rules. They were not allowed to
wear wool, drink wine or pick up anything they had dropped! Eating
beans was also strictly forbidden!
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A right angled triangle
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Draw a square on each side. A Pythagorean Puzzle
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c b a Measure the length of each side A Pythagorean Puzzle
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Work out the area of each square. a b C b a c
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c b a
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1
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1 2
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1 2
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1 2 3
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1 2 3
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1 23 4
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1 23 4
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1 23 4 5
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1 23 4 5 What does this tell you about the areas of the three
squares? The red square and the yellow square together cover the
green square exactly. The square on the longest side is equal in
area to the sum of the squares on the other two sides.
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1 23 4 5 Put the pieces back where they came from.
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1 23 4 5
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1 23 4 5
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1 23 4 5
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1 23 4 5
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1 23 4 5
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This is called Pythagoras Theorem. c b a c=a+b
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It only works with right-angled triangles. hypotenuse The
longest side, which is always opposite the right-angle, has a
special name: This is the name of Pythagoras most famous
discovery.
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c b a c=a+b
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c a c c b b b a a c y a
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1m 8m What is the length of the slope?
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1m 8m c b= a= c=a+ b c=1+ 8 c=1 + 64 c=65
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How do we find c? We need to use the square root button on the
calculator. It looks like this Press c=65 , Enter 65 = So c= 65 =
8.1 m (1 d.p.)
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c 12cm 9cm a b c=a+ b c=12+ 9 c=144 + 81 c= 225 c = 225=
15cm
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c 6m 4m s a b c=a+ b s=4+ 6 s=16 + 36 s= 52 s = 52 =7.2m (1
d.p.)
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7m 5m h c a b c=a+ b 7=a+ 5 49=a + 25
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We need to get a on its own. Remember, change side, change
sign! + 25 49 - 25 = a a= 24 a = 24 = 4.9 m (1 d.p.)
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169 = w + 36 c w 6m 13m a b c= a+ b 13= a+ 6 169 36 = a a = 133
= 11.5m (1 d.p.) a= 133 169 = a + 36 Change side, change sign!
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c b c= a+ b 11= 9+ b 121 = 81 + b 121 81 = b b = 40 = 6.3cm (1
d.p.) b= 40 a 9cm P 11cm R Q 81 Change side, change sign!
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c a b c=a+ b c=5+ 7 c=25 + 49 c= 74 c = 74 =8.6m (1 d.p.) 14m
5m r r 7m of 14 ?
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c a b 23cm 38cm p 23cm c= a+ b 38= a+ 23 1444 = a+ 529 1444 529
= y a = 915 a= 915 So a =2 x 915 = 60.5cm (1d.p.) + 529 Change
side, change sign!
