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
_______ 2)
JK

KL
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
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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

3
2 1
19) If x
3
= y

2
2
, then x

3
3
= y
 
2

2 y
2
Use the proportion a b

3
to complete each statement.
5
20) 5 a = 3b 21)
5 b
=
3 a
Find the value of x.
22) a
 b b
=
3

5

8
5 5
23)
5
3
= b a
24)
3 x
=
2
5
2x = 15 x = 7.5
25)
3
5
=
7 x

1
3(x – 1) = 35
3x – 3 = 35 x = 38/3
26)
21
= x
7
4
7x = 84 x = 12
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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

6 x 5 y

6
15 5
27

6 z 5
6x = 150 5y = 90 6z = 135 x = 25 y = 18 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 triangles are similar) x .
3
(Since the two parallel lines create congruent corresponding 1 angles, we can assume these
5 x
3


3 1 5
5
 x

3

4 5
5
 x
3(5 + x) = 20
15 + 3x = 20
3x = 5
x =
5
3
29) Complete each statement.
A
a) ∆ ABC ~ Δ EBD
3
3
 x

4
7 y

4
8 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
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