Cambridge International Mathematics

‘In proportion’

means ‘in the

same ratio’.

3cm

4cm

xcm 6cm

4cm

5cm

7cm

xcm

5cm

8cm

3cm

xcm

xm 7m 11 m

5m

12 m

2m 8m

A

B

D

C

E

F

H

G

4m

6m

3.6 m

Similarity (Chapter 18) 369

EXERCISE 18A

1 Solve forx:

a x:6=2:15 b x:5=7:31 c x:8=9:102

2 Findxgiven that the figures are similar:

ab

cd

3aIf a line of length 2 cm is enlarged with scale factor 3 , find its new length.

b A 3 cm length has been enlarged to 4 : 5 cm. Find the scale factork.

4 Comment on the truth of the following statements. For any statement which is false you should justify

your answer with an illustration.

a All circles are similar. b All ellipses are similar.

c All squares are similar. d All rectangles are similar.

5 The diagram shows a 2 m wide path around a 12 mby 8 m

swimming pool.

Are the two rectangles similar? Justify your answer.

6 Rectangles ABCD and FGHE are similar.

Find the length of FG.

7 Sketch two polygons that:

a are equiangular, but not similar

b have sides in proportion, but are not similar.

8 Can you draw two triangles which are equiangular

but not similar?

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Y:\HAESE\IGCSE01\IG01_18\369IGCSE01_18.CDR Tuesday, 28 October 2008 9:31:59 AM PETER