Cambridge International Mathematics

Similarity (Chapter 18) 371

EXERCISE 18B.1

1 Show that the following figures possess similar triangles:

abc

de f

FINDING SIDE LENGTHS

Once we have established that two triangles are similar, we may use the fact that corresponding sides are in

the same ratio to find unknown lengths.

Example 3 Self Tutor

Establish that a pair of triangles

is similar and findx:

® 1 =® 2 fcorresponding anglesg

̄ 1 = ̄ 2 fcorresponding anglesg

So,¢s ABE and ACD are similar and

BE

CD

=

AB

AC

=

AE

AD

fsame ratiog

)

x

7

=

6

10

) x= 106 £7=4: 2

When solving similar triangle problems, it may be useful to use the following method, written in the context

of the example above:

R

PT

Q S

B

40 o^40

o

C

E

A D

X W

V

U Y

24°

24°

J

K

L

M

N

A

B

C

D E

70°

70°

C B A

D

E

xcm

7cm

4cm

6cm

A

B

C D

E

C D

B

xcm

E

7cm

4cm

6cm

A

a 1 b 1

a 2 b 2

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y:\HAESE\IGCSE01\IG01_18\371IGCSE01_18.CDR Friday, 3 October 2008 12:48:39 PM PETER