Checking Scale
Factor for
Similarity
Similarity (~)
Two figures are said to be similar (~)
if one can be mapped onto the
other using a dilation followed by a
transformation; or a transformation
followed by a dilation. (same
shape, different sizes)
Corresponding Sides
NOTE: We can’t use just any two sides to calculate
scale factor, we need to look at corresponding sides.
Corresponding sides: Sides that are in the same
relative position.
So, AB corresponds to LG; AT corresponds to GR; and
BT corresponds to LR
L
A
10 m
B
8m
16 m
R
7m
14 m
T
G
20 m
Checking for similarity.
• Shapes that are similar have a set ratio between
their corresponding sides.
• A Ratio is a comparison of the size of one number
to another.
• A Proportion is a statement that sets two ratios
equal to each other.
• When two figures are similar their corresponding
parts can be put into an extended proportion that
1
2
4
holds true. Ex. = =
2
4
8
Scale Factor
The ratio of corresponding side lengths of a figure and its
image after dilation should hold true for ALL corresponding
sides.
Determine the scale factor and use it to check for similarity.
First determine the corresponding sides.
Second, check that the ratio for each pair is the same.
L
A
10 m
B
8m
16 m
R
7m
14 m
T
G
20 m
Example 1
Are the two triangles similar?
A
F
4 cm
7.5 cm
6 cm
E
C
B
2 cm
3 cm
D
5 cm
Example 2
Are the two polygons similar?
G
15 cm
A
H
E
C
B
6 cm
8 cm
3 cm
D
F
Example 3
Are the two polygons similar?
Triangle ABC has side lengths of: 5,12,13
Triangle DEF has side lengths of: 65,60,25
Example 4
• Joe and Jim are trying to guess how tall a tree in the
park is. They use a piece of rope to determine that the
tree’s shadow is 112 ft long. Joe is 5 ft tall and casts a 7
ft shadow. Set up a diagram and use it to determine the
height of the tree.
X
5
7
112