Cambridge International Mathematics

The Egyptians used this procedure to construct their right angles:

make rope taut

corner

line of one side

take hold of knots at arrows of building

hypotenuse

legs

c c

cX a

aaX

bX b

b GEOMETRYPACKAGE

170 The theorem of Pythagoras (Chapter 8)

Aright angled triangleis a triangle which has a right angle

as one of its angles.

The sideoppositetheright angleis called thehypotenuse

and is thelongestside of the triangle.

The other two sides are called thelegsof the triangle.

Around 500 BC, the Greek mathematicianPythagoras

discovered a rule which connects the lengths of the sides of

all right angled triangles. It is thought that he discovered the

rule while studying tessellations of tiles on bathroom floors.

Such patterns, like the one illustrated, were common on the

walls and floors of bathrooms in ancientGreece.

PYTHAGORAS’ THEOREM

In a right angled triangle with

hypotenusecand legsaandb,

c^2 =a^2 +b^2.

In geometric form,Pythagoras’ theoremis:

In any right angled triangle, the area of the

square on the hypotenuse is equal to the

sum of the areas of the squares on the other

two sides.

A PYTHAGORAS’ THEOREM [4.6]

c

b

a

By looking at the

tile pattern above,

can you see how

Pythagoras may

have discovered

the rule?

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y:\HAESE\IGCSE01\IG01_08\170IGCSE01_08.CDR Wednesday, 17 September 2008 1:38:37 PM PETER