Transcript 8.2 Similarity - Chandler Unified School District

8.2 Similarity
Objective:
After studying this section, you will be able to identify
the characteristics of similar figures.
Similar—figures with the same shape but
not necessarily the same size.
Dilation—enlargement of an object.
Reduction—opposite of dilation, creates a
smaller similar object of the original object.
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.
H
20 cm
2 cm
5 cm
Definition
Similar Polygons are
polygons in which
1. The ratios of the
measures of corresponding
sides are equal
2. Corresponding angles
are congruent
Triangle MCN is a
dilation of triangle
MED, with an
enlargement ratio
of 2:1 for each pair
of corresponding
sides. Find the
lengths of the sides
of triangle MCN
C (0,8)
E
(0,4)
(0,0)
M
(3,0)
D
(6,0)
N
Given ABCD is similar
to EFGH with
measures shown
6
F
B
4
A
9
C
7
3
E
G
D
Find FG, GH, and EH
H
Theorem
The ratio of the perimeters
of two similar polygons
equals the ratio of any pair
of corresponding sides
Given triangle JHK is similar to triangle
1
POM, H  90, J  40, M  ( x  5), O  y
2
Find x and y
M
K
H
J
O
P
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
12
T
9
D
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 A’B’C’?
P
C
15
A 12
A’
C’
10
B
B’
Summary: Explain the
difference between similar and
congruent polygons.
Homework: worksheet