Download TOPIC #2-1: EXPLORING SIMILAR POLYGONS

TOPIC 9-3: MORE SIMILAR POLYGONS
TERM
DEFINITION
Common
Ratio
SKETCH
The ratio of the lengths of two
corresponding sides.
EXAMPLE 1 Use the similar figures below to answer the
questions that follow.
D
10
A
8
5
B
6
C

H
5
E
4
2.5
F
3
G
What is the common ratio of quadrilateral ABCD to
quadrilateral EFGH above?
EXAMPLE 2 Show that the ratio of the perimeters is the same as
the common ratio.
EXAMPLE 3 What is the common ratio of quadrilateral EFGH to
quadrilateral ABCD in EXAMPLE 1?
EXAMPLE 4 Determine if the figures are similar. Justify your
answer.
37
9
18
6
12
53
3
2
EXAMPLE 5 Use the similar figures below to answer the
questions that follow.
H
A
2.5
z
B
3
12
D
x
C

E
10
5
F
y
G
a) Quad EFGH  Quad _________________.
b) What is their common ratio?_____________
c) Find the following:
 x = ____________
 y = ____________
 z = ____________
d) What is the ratio of their perimeters?__________
e) How do b) and d) compare?__________________________
EXAMPLE 6
Use the similar figures below to answer the
questions that follow.
V
U
x
R
y+2
S

T
18
E
D
3
A
5
B
4
C
a) Find the common ratio of polygon RSTUV to polygon
ABCDE:___________
b) Find the values of:
x = __________
y = __________
EXAMPLE 7 Quad ABCD  Quad EFGH below. Answer the
following questions.
21
E
A
100
60
F
B
9
5
D
6
C
H
a) Complete the following:
mE = __________
18
G
c) Find the following:
mG = __________
EH = __________
mB = __________
BC = __________
mH = __________
AB = __________
b) What is the common ratio
of Quad ABCD to Quad
EFGH?__________
EXAMPLE 8 The lengths of the sides of a triangle are in the ratio
3:5:7. Its perimeter is 120 cm. Find the length of the
shortest side of the triangle.
EXAMPLE 9 The measures of the angles of a triangle are in the
ratios 1:2:3. Find the measure of the largest angle.