Objective:

1
8.2 Similarity

• Objective
• After studying this section, you will be able to
  identify the characteristics of similar figures.

2
Similarfigures with the same shape but not
necessarily the same size.
Dilationenlargement of an object.
Reductionopposite of dilation, creates a smaller
similar object of the original object.
3
A pinhole camera produces a reduced image of a
candle. The size of the image is proportional to
the distance of the candle from the camera.
Given the measurements shown in the diagram, find
the height of the candle.
20 cm
2 cm
H
5 cm
4
Definition Similar Polygons are polygons in
which 1. The ratios of the measures of
corresponding sides are equal 2.
Corresponding angles are congruent
5
Triangle MCN is a dilation of triangle MED, with
an enlargement ratio of 21 for each pair of
corresponding sides. Find the lengths of the
sides of triangle MCN
C
(0,8)
E
(0,4)
(6,0)
(0,0)
(3,0)
M
D
N
6
Given ABCD is similar to EFGH with measures shown
F
B
6
4
9
A
C
E
7
G
3
D
Find FG, GH, and EH
H
7
Theorem The ratio of the perimeters of two
similar polygons equals the ratio of any pair
of corresponding sides
8
Given triangle JHK is similar to triangle POM,
Find x and y
M
K
J
H
P
O
9
Given Triangle BAT is similar to Triangle DOT,
OT 15, BT 12, TD 9
A
Find the value of x (AO)
x
O
15
B
D
T
12
9
10
C
P
C
In the diagram, segments PA, PB, and PC are drawn
to the vertices of triangle ABC from an external
point P, then extended to three times their
original lengths to points A, B, and C. What
are the lengths of the sides of triangle ABC?
15
10
B
A
12
B
A
11
Summary Explain the difference between similar
and congruent polygons.
Homework worksheet