WHAT IS SIMILARITY????
Similarity is the name given to two figures having the
same shape, but different sizes. In simpler words, one
figure is an enlargement of the other.
 Similarity is the quality of being similar. It refers to the
closeness of appearance between two or more objects. It
is the relation of sharing properties

DEFINITIONS






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Corresponding - similar especially in position or purpose;
equivalent
Ratio - the relationship between two numbers or quantities
(usually expressed as a quotient)
Proportion - the relation between things (or parts of things)
with respect to their comparative quantity, magnitude, or
degree
Congruent - equilateral, equal, exactly the same (size, shape,
etc.)
Enlargement - expansion: the act of increasing (something) in
size or volume or quantity or scope
Theorem - an idea accepted as a demonstrable truth
Scale factor – reduced ratio of corresponding sides of two
similar figures.
EXAMPLES
THESE TWO
SHAPES ARE
SIMILAR
CONDITIONS FOR SIMILAR TRIANGLES

SIDE ANGLE SIDE (SAS)
X
B
3 cm
A
4 cm
C
8 cm
6 cm
40°
W
Y
If a pair of corresponding sides of two
triangles are in the same proportion and the
angle between the sides are equal, then the
triangles are similar.
ANGLE ANGLE SIDE TRIANGLE
(AAS)

If the corresponding angles of two triangles are equal,
then the two triangles are similar. Y
B
A
C
X
Z
. SIDE SIDE SIDE TRIANGLES (SSS)
 In this type of similarities, the triangles are similar
when three sides of the triangle are corespnding. So,
‘if all pairs of corresponding sides of two triangles are
proportional, then triangles are similar.
 NOTE : In side side side triangles, their corresponding
sides are manified by a certain factor ,K.

X
B
3 cm
A
4 cm
6 cm
C
6 cm
W
8 cm
12 cm
Y
Circles
Regular Pentagons
Squares
Equilateral Triangles
AREAS OF SIMILAR FIGURES

The following rectangles are similar and their ratio
of corresponding sides is y. ABCD is of length b and
width a.
Y
ya
a
A

X
C
B
b
D
W
If two figures are similar and their sides are in the
ratio y, then their areas will be in the ratio y2”.
Yb
Z
• When solid objects are similar, one is an
accurate enlargement of the other.
• Thus, the corresponding sides should be in the
same ratio.
140 cm
80 cm
100 cm
48 cm
84 cm
60 cm
VOLUMES AND SURFACE AREAS OF
SIMILAR 3-D OBJECTS

A and B are two similar 3-D shapes. Their ratio of
corresponding sides is .
kc
kb
c
b
If the ratio of the corresponding
sides of two 3-D objects is k,
a
then the ratio of their surface areas is

ka
A
B
kc
kb
c
b
a
ka
A
B
• If
the ratio of the corresponding
sides of two 3-D objects is k,
then the ratio of their volumes is

When solid objects are similar, one is an accurate
enlargement of the other. If two objects are similar
and the ratio of corresponding sides (scale factor) is
k, then the ratio of their volumes is k3.

A line has one dimension, and the scale factor is
used once.

An area has two dimensions, and the scale factor is
used twice.

A surface area of 3 dimensional figures also uses
the scale factor twice.

A volume has three dimensions, and the scale
factor is used three times.
QUESTIONS
Ravina looks in a mirror and sees the top of
a building. His eyes are 1.25 m above
ground level, as shown in the following
diagram.
If Ravina is 1.5 m from the mirror and
181.5 m from the base of the building,
how high is the building?
Solution to problem
So, the height of the building is 150 m.
QUESTION
ANSWER
P= 7.2
Q= 6.4
QUESTION
SOLUTION