The theorem of

Pythagoras

8

Contents:

A Pythagoras’ theorem [4.6]

B The converse of Pythagoras’ theorem [4.6]

C Problem solving [4.6]

D Circle problems

E Three-dimensional problems [4.6]

Opening problem

The Louvre Pyramid in Paris, France has a square base

with edges 35 m long. The pyramid is 20 : 6 m high.

Can you find the length of the slant edges of the pyramid?

The ancientEgyptiansused a rope with 12 equally

spaced knots to form a triangle with sides in the ratio

3:4:5:

This triangle has a right angle between the sides of

length 3 and 4 units.

In fact, this is the simplest right angled triangle with

sides of integer length.

Right angles ( angles) are used when constructing buildings and dividing areas of land into rectangular

regions.

90 o

[4.6, 4.7]

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Y:\HAESE\IGCSE01\IG01_08\169IGCSE01_08.CDR Tuesday, 23 September 2008 9:09:58 AM PETER