Download Ratios: the quotient of two numbers, a ÷ b, usually

GEOMETRY/TRIGONOMETRY 2
Name _______________________
Ratios: the quotient of two numbers, a  b, usually written
a
b
or a:b, b  0.
 simplest form: each term of the ratio is reduced by their _____________________.
 Ratios can be used to compare numbers, such as lengths or angle measures, but the
quantities being compared must be in the same __________.
 Ratios have no units.
 Ratios can be used to compare three or more numbers, i.e., a:b:c.
Proportions:

a
b

an equation that states that two ratios are _______________.
c
d
a:b = c:d
 _______________: the first and last terms of a proportion
 _______________: the middle terms of a proportion
 Properties of Proportions (“a prop. of prop.”)
 means-extremes property: the _______________ of the means is equal to the
_______________ of the extremes. If
 interchange the means:
If
 reciprocal of the ratios:
If
 add 1 to both sides:
If
2
3
2
3
2
3
2
3




4
6
4
6
4
6
4
6
, then _____ = _____
, then _____ = _____
, then _____ = _____
, then _____ = _____
Express each ratio in simplest form.
1) AB:AC
________
2)
mB
mA
3) the measure of the largest angle
to the smallest angle
A
________
12
91°
24
________
B
26°
27
C
Express the ratio AB: AD in simplest form.
(4)
(5)
(6)
AB
12 cm
1m
25 cm
AD
15 cm
0.3 m
2m
AB:AD
:
:
:
In exercises 7-9, find the measure of each angle.
7) Two complementary angles have measures in the ratio 2:3
7) __________
8) The measures of the angles of a triangle are in the ratio 2:2:5.
8) __________
9) The ratio of the measures of the exterior angles of a pentagon is
2:3:4:4:5. Find the measure of the largest interior angle.
9) __________
Complete and name the property of proportions you used.
10) If
12) If
x
5
8
y

3
, then 2x = _____
2
11) If

y
3
, then
= _____
x
8
13) If
14) If 4:x = y:8, then 8:x = _____
a)
4

7
21
b)
a7
7
7
7
x

x7
y
, then
= _____
8
7

3
4
, then 3x = _____
15) If 4:x = y:8, then xy = _____
16) Which proportions are equivalent to
a
x

25
21
a
7

4
?
21
c)
7
a

21
4
d)
21
a

7
4
Use the means-extreme property to find the value of x.
17)
20)
6
x

x-5
2
3
5
18)

5
6
In the figure
21)
AD
DC

AB
.
BC
AD
DC
23)
4
6
24)
8
25)
18
20

x-2
x 1
9
2x

x2
19)
1
4
12
x -1
22)
x3

1
2

3
5
Complete the table.
AC
AB
B
BC
8
13
16
18
15
24
A
D
C