Cambridge International Mathematics

Similarity (Chapter 18) 373

gh i

The properties of similar triangles have been known since ancient times. But even with the technologically

advanced measuring instruments available today, similar triangles are important for finding heights and

distances which would otherwise be difficult to measure.

Step1: Read the question carefully and draw a sketch

showing all the given information.

Step2: Introduce a variable or unknown such asx,to

represent the quantity to be found.

Step3: Set up an equation involving the unknown and

then solve for the unknown.

Step4: Answer the question in a sentence.

Example 5 Self Tutor

Find the height of the pine tree:

contains similar triangles and

)

x

1

=

12

2

) x=6

So, the pine is 6 m high.

C PROBLEM SOLVING [4.5]

Diagrams are very

important. They often help

you to solve the problem.

Make sure your diagrams

are large enough.

a a

5cm

3cm

4cm xcm

A

D

B

E C

xcm

8cm

9cm

10 cm

50°

50°

S

R

Q

T

P

2cm

5cm

xcm

X

Y Z

U V

1m

2m 10 m

shadow

stick

xm

1

2

x

1

2 10

x

12

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y:\HAESE\IGCSE01\IG01_18\373IGCSE01_18.CDR Friday, 3 October 2008 12:54:45 PM PETER