9.40 Chapter 9
similar figures ЧྡҖ
9.4 Similar Plane Figures
In Book 1B Chapter 10, we learnt the concepts of similar triangles. Now,
let's consider other figures.
The following polygons ABCD and EFGH have the same shape. They are
called a pair of similar polygons, which are a kind of similar figures .
A
B
C D
E
F
G H
By measuring their sizes of angles and the lengths of sides using a
protractor and a ruler respectively, we note that:
(i) +A = +E, +B = +F, +C = +G, +D = +H
They are four pairs of corresponding angles of polygons ABCD and
EFGH.
(ii) AB
EF = BC
FG = CD
GH = DA
HE
We say that the four pairs of corresponding sides of polygons ABCD
and EFGH are proportional.
In fact, two polygons with their corresponding angles equal and their
corresponding sides proportional are similar polygons.
Note: (a) A pair of congruent figures must also be a pair of similar
figures.
(b) All circles are similar figures. For example:
(c) Regular polygons with the same number of sides are similar figures. For example:
(i) (ii) (iii)
Equilateral triangles Squares Regular pentagons