Learn about the Pythagoras Theorem Apply the Pythagoras Theorem to solve the triangles Students and Teachers will be able to

Pythagoras was a Greek philosopher and religious leader. He was responsible for many important developments in maths, astronomy, and music.

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.

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!

A right angled triangle

Draw a square on each side. A Pythagorean Puzzle

c b a Measure the length of each side A Pythagorean Puzzle

Work out the area of each square. a b C² b² a² c

c² b² a²

1 

1 2 

1 2 

1 2 3 

1 2 3 



1 23 4

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.

Put the pieces back where they came from.

This is called Pythagoras’ Theorem. c² b² a² c²=a²+b²

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.

c b a c²=a²+b²

c a c c b b b a a c y a

1m 8m What is the length of the slope?

1m 8m c b= a= c²=a²+ b² c²=1²+ 8² c²= c²=65

How do we find c? We need to use the square root button on the calculator. It looks like this √ Press c²=65 √, Enter 65 = So c= √ 65 = 8.1 m (1 d.p.)

c 12cm 9cm a b c²=a²+ b² c²=12²+ 9² c²= c²= 225 c = √ 225= 15cm

c 6m 4m s a b c²=a²+ b² s²=4²+ 6² s²= s²= 52 s = √ 52 =7.2m (1 d.p.)

7m 5m h c a b c²=a²+ b² 7²=a²+ 5² 49=a² + 25

We need to get a² on its own. Remember, change side, change sign! = a² a²= 24 a = √ 24 = 4.9 m (1 d.p.)

169 = w² + 36 c w 6m 13m a b c²= a²+ b² 13²= a²+ 6² 169 – 36 = a² a = √ 133 = 11.5m (1 d.p.) a²= = a² + 36 Change side, change sign!

c b c²= a²+ b² 11²= 9²+ b² 121 = 81 + b² 121 – 81 = b² b = √ 40 = 6.3cm (1 d.p.) b²= 40 a 9cm P 11cm R Q 81 Change side, change sign!

c a b c²=a²+ b² c²=5²+ 7² c²= c²= 74 c = √ 74 =8.6m (1 d.p.) 14m 5m r r 7m ½ of 14 ?

c a b 23cm 38cm p 23cm c²= a²+ b² 38²= a²+ 23² 1444 = a² – 529 = y² a = √ 915 a²= 915 So a =2 x √ 915 = 60.5cm (1d.p.) Change side, change sign!