Cambridge International Mathematics

370 Similarity (Chapter 18)

If two triangles are equiangular then they aresimilar.

Similar triangles have corresponding sides in the same ratio.

If two triangles are equiangular then one of

them must be an enlargement of the other.

For example, ¢ABC issimilarto¢PQR.

So,

QR

BC

=

RP

CA

=

PQ

AB

where each fraction equals the scale factor of the enlargement.

To establish that two triangles aresimilar, we need to show that they areequiangular

or that theirsides are in proportion.

You should note that:

² either of these properties is sufficient to prove that two triangles are similar.

² if two angles of one triangle are equal in size to two angles of the other triangle then the remaining

angles of the triangles are equal.

Example 2 Self Tutor

Show that the following figures possess similar triangles:

ab

a ¢s ABC and DBE are equiangular as:

² ® 1 =® 2 fequal corresponding anglesg

² angle B is common to both triangles

) the triangles are similar.

b ¢s PQR and STR are equiangular as:

² ® 1 =® 2 fgiveng

² ̄ 1 = ̄ 2 fvertically opposite anglesg

) the triangles are similar.

B SIMILAR TRIANGLES [4.5]

A

B 40° C

60°

80°

P

Q 40° R

60°

80°

B E

D

A

C

B E

D

A

C

a 1

a 2

P

Q T

a a

R

S

P

Q T

a 2

b 2

a 1

b 1

R

S

In the previous exercise, you should have found that:

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
y:\HAESE\IGCSE01\IG01_18\370IGCSE01_18.CDR Wednesday, 8 October 2008 10:11:46 AM PETER