Download Geo_Lesson 8_3

Geometry Lesson 8.3
Similar Polygons
1. Similar Polygons


Two polygons are
similar if their
 Corresponding
angles are
congruent
 Corresponding
side lengths are
proportional
Use the ~ symbol
for similarity
G
f is a scale fx
F
factor
C
x
B
fw
y
w
A
fy
z
D
E
fz
H
ABCD ~ EFGH
Similarity Statement:
A  E, B  F
C  G, D  H
AB BC CD DA



EF FG GH HE
Example 2


Determine if the figures are similar
If so, write a similarity statement
Corresponding s ?
A  N, R  T, X  M
Corresponding sides
proportional?
AX 9 3
 
NM 6 2
XR 15 3


MT 10 2
RA 12 3


TN 8 2
Yes, angles 
and sides
proportional
AXR ~ NMT
Practice 2
Determine if the figures are similar
 If so, write a similarity statement
(a)
(b)

No: sides not proportional
(c)
No: s not 
Yes: all s  and sides
proportional (4/3 ratio)
LMN ~ TPO
Example 3




You just got a job at Kinko’s and a customer
wants to enlarge a photo to create a poster
The photo is a rectangle 3 in high x 5 in wide
5 in
Kinko’s poster paper is 16 in tall
What is the scale factor (large : small)? 3 in
W
16 in
f 
 5.33
3 in
How wide must the poster paper be? =
16 in
16 in x in

3 in 5 in
W  26.67 in
(at least 27 in wide)
Practice 3



Your family just got a
50 inch plasma HDTV
However, your friend
got an even bigger
72 inch HDTV
If the TVs are similar
rectangles (same
aspect ratio) and
your picture is 24.5
inches tall, how tall is
your friend’s picture?
yours
24.5 in
your friend’s
h
24.5 50

h
72
h  35.28 in
Example 4 / Practice 4

Find x and y for the similar polygons
(a)
(b)
x 6

6 4
y 6

8 4
4x = 36
x=9
4y = 48
y = 12
x = 13.5
y = 16 (direct)
2. Perimeter of Similar Polygons

If two polygons are similar, then the
ratio of their perimeters = ratio of
corresponding side lengths
G
F
C
PABCD AB BC CD DA




PEFGH EF FG GH HE
B
A
If ABCD ~ EFGH, then
D
E
H
Example 5


ABC ~ QRS
What is the perimeter of QRS?
R
B
9
5
A
7
10
C
Q
PQRS 10
 2
PABC 5
PQRS = 2PABC
S PQRS = 2(5+7+9)
PQRS = 2(21)
PQRS = 42
Assignment
8.3 w/s