Download Corresponding Angles

An in Depth Look at Ratios and
Proportions and Their
Applications
Ratios
Special
Ratios
Equal
Ratios
Proportions
Constant
Ratios
are the comparison of two
or more numbers.
Which ratio shows the ratio of 2 fish to 3 bear?
A
B
C
D
E
Which ratio shows the ratio of 1
soccer ball to 3 basketball?
A
B
C
D
E
Which ratio shows the ratio of 3
butterflies to 1 apple?
A
B
C
D
E
Three Ways to Write a
Ratio
The ratio of 3 boys to 5 girls
can be written as:
a) 3 to 5
b) 3: 5
3
c)
5
Equal ratios are like
equivalent fractions.
They name the same
quantity.
Examples of Equal Ratios:
3 6

5 10
3 75

4 100
Two equal ratios form
a proportion.
In a proportion the
product of the means is
equal to product of the
extremes.
3 : 5 = 6 : 10
Means
Extremes
3 6

5 10
Means
Extremes
6 x 5 = 3 x 10
30 = 30
Determine if the following
are proportions.
1)
5 60

3 36
2)
8 4

15 8
5 60

3 36
8 4

15 8
3 x 60 = 5 x 36 4 x 15 = 8 x 8
180 = 180
60  64
Yes, it is a proportion.
No, it is not a proportion.
Corresponding sides of Similar
Triangles have the same ratio.
Corresponding Angles of Similar
Triangles have congruent angles
Triangle
Triangle
A
A is similar to
D
D
E
B
A
C
D
AB BC AC


DE EF EF
F
<A <D
<B  <E
<C  <F
D
A
5
4
C
3
y
x
B
F
6
E
Use a proportion to find x and y.
AC CB

DF FE
CB
AB

FE
DE
4 3

x 6
3
5

6
y
4  6  3 x
3 y  5 6
24  3x
3 y  30
24
3x

3
3
3y
30

3
3
8 x
y  10
Another type of special
ratio is a constant ratio or
rate.
Distance = rate x time
is an example of a constant
ratio.
Time
1
2
3
4
Distance 60 120 180 240
distance
d=rxt
300
250
200
150
100
50
0
1
2
3
time
4