height

radius

Similarity

18

Contents:

A Similarity [4.5]

B Similar triangles [4.5]

C Problem solving [4.5]

D Area and volume of similar shapes [4.5]

Opening problem

#endboxedheading

Jacob makes cylindrical tanks of different sizes. His smallest tank

has a height of 2 m and a radius of 0 : 8 m. If he wants to manufacture

another tank in the same proportions but with a base radius of 1 m,

find the:

a height of the new tank

b ratio of the i surface areas ii capacities.

We have seen previously that two figures arecongruentif they are identical in every respect apart from

position. In this chapter we discusssimilarity, which is a closely related topic. It deals with figures that

differ in size but have the same proportions.

Two figures aresimilarif one is an enlargement of the other, regardless of their orientation.

If two figures are similar then their corresponding sides arein proportion. This means that the lengths of

sides will be increased (or decreased) by the same ratio from one figure to the next. This ratio is called the

scale factorof the enlargement.

A SIMILARITY [4.5]

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y:\HAESE\IGCSE01\IG01_18\367IGCSE01_18.CDR Friday, 10 October 2008 9:31:34 AM PETER