Congruence and Similarity (II) 9.41
In Book 1B Chapter 10, we learnt that in two similar triangles,
(a) their corresponding angles are equal;
(b) their corresponding sides are proportional.
Likewise,
in two similar figures,
(a) their corresponding angles are equal;
(b) their corresponding sides are proportional.
In this section, we focus on
similar polygons only. All
'similar figures' refer to
'similar polygons' unless
otherwise stated.
◀
As shown below, quadrilaterals ABCD and PQRS are similar figures.
B
A5 cm
2 cm
3 cm
6 cm
D
C
Q
P7.5 cm
3 cm
4.5 cm
9 cm
SR
In the above case, similar figures ABCD and PQRS can be represented as
follows:
ABCD + PQRS
Quick Quiz
In the figure, ABCD + PQRS. Complete the following.
(a) +BAD = + , +ABC = + ,
+BCD = + , +ADC = +
(b) ()
AB = ()
BC = ()
CD = ()
DA
C
B
A
D
P
S
R
Q
1. +A = +P, +B = +Q,
+C = +R, +D = +S,
i.e. their corresponding angles
are equal.
2. PQ
AB = QR
BC = RS
CD = SP
DA = 3
2 ,
i.e. their corresponding sides
are proportional.
◀
We must name the pair of similar
figures according to the order of
the corresponding vertices, such
that the corresponding angles and
sides are identified easily.