Cambridge International Mathematics

372 Similarity (Chapter 18)

Step 1: Label equal angles.

Step 2: Put the information in table form, showing the equal

angles and the sides opposite these angles.

Step 3: Since the triangles are equiangular, they are similar.

Step 4: Use the columns to write down the equation for the ratio

of the corresponding sides.

Step 5: Solve the equation.

® ̄ ²

• 6 x small¢


• 10 7 large¢

from which

6

10

=

x

7

) x=4: 2

Example 4 Self Tutor

Establish that a pair of triangles is

similar, then findxif BD=20cm:

® ̄ ²

• x+2 x small¢


• 20 12 large¢

The triangles are equiangular and hence similar.

)

x+2

20

=

x

12

fsame ratiog

) 12(x+2)=20x

) 12 x+24=20x

) 24 = 8x

) x=3

EXERCISE 18B.2

1 In the following, establish that a pair of triangles is similar, then findx:

abc

de f

2cm

3cm

6cm

xcm

A

B C

DE

5cm

7cm 2cm

xcm

P

Q R S

T

6cm

5cm 6cm

xcm

U

V

Y

X

Z

A

E

B C D

xcm

12 cm

()x¡+¡2 cm

a

a

A

E

B C D

xcm

12 cm

()x¡+¡2 cm

a

a

b

b

20 cm

xcm

6cm 3cm

5cm

5cm 3cm

xcm

7cm

1cm

10 cm

2cm

xcm

IGCSE01

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y:\HAESE\IGCSE01\IG01_18\372IGCSE01_18.CDR Friday, 3 October 2008 12:51:29 PM PETER