Class Notes Date:
7.2
– RATIO, PROPORTION, & SIMILARITY
________: quotient of two numbers,
a
÷
b
, usually written as
a
to
b
,
a
:
b
, or
a b
simplest form.
, in
EXAMPLES
Express each ratio in simplest form.
K
8
L
_______ 1)
JK
to
KL
10 10
JK

KL
_______ 2)
ML
_______ 3)
m

K
:
m

L
J
12
M
For #1-5
_______ 4)
m

M
:
m

J
_______ 5)
KL
: perimeter
JKLM
Ratios can be used to compare numbers, such as lengths or angle measures, but the quantities being compared
must be in the same units
.
_______ 6) A sheet of plywood is
0.5 m
long by
35 cm
wide. Find the ratio of
length to width.
Express each ratio in simplest form.
_______ 7)
15
f
20
f
_______ 8)
Write each ratio if x = 2, y = 3, and z = 4.
4
x x
2
_______ 9)
x
to
y
_______ 10)
x
+
z
:
y
_______ 11)
x
:
x
+
y
:
x
+
_______ 12) Two complementary angles have measures in the ratio of 2:7.
Find the measure of each angle.
_______ 13) The measures of the five angles of a pentagon are in the ratio
11:7:5:4:3. Find the measure of each angle.
z
Page 1

Class Notes Date:
PROPERTIES OF PROPORTIONS
Proportion : an equation stating that two ratios are equal
a b c
=
d
or
a
:
b
=
c
:
d a
is the 1st term
b
is the 2nd term
c
is the 3rd term
a
and
d
are called the extremes
d
is the 4th term
EXAMPLES
Complete each statement.
14) If
x
: 4 = 3 : 7, then 7
x
= 12
b
and
c
are called the means
15) If
3
x y
=
8
, then
x y
= _______ OMIT
2
16) If 2
x
= 3
y
, then
3
=
y x
18) If
x
7
=
4
2
, then
x

7
7
=
4

2
2

6
2

3
1
19) If
x
3
=
y

2
2
, then
x

3
3
=
y
2
2

y
2
Use the proportion
a b

3
5
to complete each statement.
20) 5
a
= 3b 21)
5
b
=
3
a
Find the value of x.
22)
a

b
=
b
3

5
5

8
5
23)
5
3
=
b a
24)
3
x
=
2
5
2x = 15 x = 7.5
25)
3
5
=
x
7

1
3(x
– 1) = 35
3x
– 3 = 35 x = 38/3
26)
21
=
x
7
4
7x = 84 x = 12
Page 2

Class Notes Date:
Similar polygons ( ~ ): polygons that have the same shape but not
necessarily the same size
To be similar, two polygons must meet the following conditions:
1) They have the same shape.
2) Corresponding angles are congruent.
3) Corresponding sides are proportional.
The ratio of the lengths of any two corresponding sides is called the similarity ratio .
EXAMPLES
27) quad
ABCD
~ quad
A B C D
. Find the similarity ratio of I to II and then
x
,
y
,
and
z
.
I : II = 24 : 20 = 6 : 5
30
x

6
5
y
15

6
5
6x = 150 x = 25
5y = 90
y = 18
27

z
6
5
6z = 135
z = 22.5
A
27
24
D
I
y
B
30
C
A

z
20
D

II
15
x
C

28) Find the value of
(Since the two parallel lines
3 create congruent corresponding angles, we can assume these triangles are similar)
x
.
1
5
x
3

5
5

x

3(5 + x) = 20
3
4
15 + 3x = 20
3x = 5
x =
5
3

5
5

x
29) Complete each statement.
A
a)
∆
ABC
~
Δ
EBD
3
3

x

4
7
y
8

4
7
8
x
E
b)
x
= ______
y
3 12 + 4x = 21 7y = 32 c)
y
= ______
C
3
D
4
B
4x = 9
x

9
4

2.25
y

32
7

4
4
7
Page 3