Download Ratios Proportions Similarity and Practice

Geometry
Name: __________________________
Unit 6 – Similarity
Date: ___________________________
Ratio - ________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Examples: ______________
________________
Ratios can be written in three different ways:
1.)
2.)
3.)
These are all equivalent ratios and they represent the ratio of ______________________
______________________________________________________________________
Ratios are usually expressed in simplest form. This means that for a final answer you should
reduce all ratios. You reduce ratios just like you would reduce a fraction.
Ex1:
Ex2:
Ex3:
When simplifying ratios, the units of each number must be the same.
Ex1:
Ex2:
Geometry
Name: __________________________
Unit 6 – Similarity
Date: ___________________________
How can we apply ratios to word problems?
Example 1: The ratio of two supplementary angles is _____________. Find the measure of
each angle.
Steps for completing ratio word problems:
1. __________________________________________________________
2. __________________________________________________________
3. __________________________________________________________
4. __________________________________________________________
Example 2: The measure of the angles in a triangle are in the ratio ________________.
Find the measure of each angle.
Example 3: ___________ prize money is to be allotted to the first, second, and third place
winners of a competition in the ratio __________________. Determine how much money
each winner should receive.
Geometry
Name: __________________________
Unit 6 – Similarity
Date: ___________________________
Proportion - ____________________________________________________________
______________________________________________________________________
Ex1:
Ex2:
We can use algebra to solve for unknowns within proportions. To solve a proportion you must:
1. __________________________________________________________
2. __________________________________________________________
3. __________________________________________________________
4. __________________________________________________________
Ex1.
Ex2.
Ex3.
Ex4.
Ex5.
Geometry
Name: __________________________
Unit 6 – Similarity
Date: ___________________________
Where else do we see ratios and proportions?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Example: ______________________________________________________________
______________________________________________________________________
______________________________________________________________________
Ex 1. On a map every _______ equals ________. You measure the distance between your
house and your friend’s house as _________ on the map. How many miles apart do you really
live?
Ex 2. On a scale drawing every _________ represents ________. If you measure an object
on the drawing as ________, how long is it really?
Ex 3. On a blueprint _______ equals ________. If a room is really ________ long, how long
would it appear on the blueprint?
Ex 4. If ______ bags of apples cost ________, then how much does ________ bags of
apples cost?
Geometry
Name: ___________________________________
Unit 6 WS 5 (Ratios)
Date: ____________________________________
Directions: Simplify each ratio.
1.
15
35
2.
21
14
3.
55
11
4.
52
8
5.
5a
10a
6.
2a 2
34a 3
7.
22a 4b
55ab 2
8.
37a 7b
51a 5
9.
42cm
1m
10.
18mm
3cm
11.
13.
15in
3ft
14.
4ft
16in
15.
2km
350m
1760ft
1mi
12.
5m
324cm
16.
15ft
3yd
Geometry
Name: ___________________________________
Unit 6 WS 5 (Ratio Apps)
Date: ____________________________________
Directions: Solve each word problem. Show all work; label all answers.
1. The ratio of two complementary angles is
2:3. Find the measure of each angle.
2. The ratio of the six angles in a hexagon
(1, 2, 3, 4, 5, and 6) is
2:2:3:3:4:4. Find the measure of each
angle.
m1 = _______
m2 = _______
m3 = _______
m4 = _______
m1 = _______
m5 = _______
m2 = _______
m6 = _______
3. The interior angle measures of a
quadrilateral (1, 2, 3, and 4) are in
the ratio 3:4:5:6. Find the measure of
each angle.
4. The ratio of two supplementary angles is
4:5. Find the measure of each angle.
m1 = _______
m2 = _______
m3 = _______
m1 = _______
m4 = _______
m2 = _______
5. Prize money for a contest must be allotted in the
following ratio to the top five winners: 6:4:3:2:1.
The total amount of prize money is $5,000.
Determine how much money each person receives.
6. Three students get in trouble at school. They
must serve a total of 18 hours of detention. The
detentions will be allotted in the ratio 2:3:4 for
Adam, Alan, and Aaron respectively. Determine
how much time each student will serve.
First: __________
Second: ________
Third: _________
Adam: _______
Fourth: ________
Alan: ________
Fifth: __________
Aaron: _______
Geometry
Name: ___________________________________
Unit 6 WS 6 (Proportions)
Date: ____________________________________
Directions: Solve each proportion.
1.
5.
x
6

2 12
2 3x

5
7
2.
3 9

5 x
3.
2x 12

5
15
4.
8 2

x 5
6.
x 5 1

4
2
7.
x 3 4

2
3
8.
x
4

7 2
9.
x 2 4

x 3 5
10.
x  3 2x  1

2
3
11.
x 4 6

x 4 5
12.
3x  5 18x  5

3
7
Geometry
Name: ___________________________________
Unit 6 WS 6 (Proportion Apps)
Date: ____________________________________
Directions: Solve each proportion word problem. Show all work; label all answer.
1. If 6 pounds of apples cost $9, then how
much would 21 pounds of apples cost?
Answer: ______________
3. If $24 worth of fertilizer covers 5,000
square feet, then how much would it cost
to cover 30,000 square feet?
2. The scale on a map is 1 inch equals 5 feet.
What is the distance between two points
on the map that are 8 1/2 inches apart on
the map?
Answer: ______________
4. If a chain link fence costs $180 for 20
feet installed, how much would it cost to
install 300 feet?
Answer: ______________
Answer: ______________
5. A store makes a profit of $15,000 for
every 300 coats that they sell. If they
make a profit of $25,000, how many coats
did they sell?
6. Last week you earned $262.90 after
working 22 hours. How much will you earn
this week if you have worked 15 hours.
Answer: ______________
Answer: ______________
Geometry
Name: __________________________
Unit 6 – Similarity
Date: ___________________________
Similarity: _____________________________________________________________
______________________________________________________________________
1. __________________________________________________________
____________________________________________________________
2. __________________________________________________________
____________________________________________________________
The symbol for similarity is: _______.
Example 1:
Ex2.
If ABCD ~ WXYZ, then…
A @ _______
B @ __________
C @ _______
D @ __________
AB

BC

CD

DA
page 9
Geometry
Name: __________________________
Unit 6 – Similarity
Date: ___________________________
Ex3.
If DDOG ~ DCAT, then all corresponding angles are congruent.
Also, all sides are in proportion (share the same scale factor).
The scale factor of DDOG to DCAT is ___________. In other words, all of the
corresponding sides will form ratios equivalent to ___________.
Name the similar figures.
Ex4.
Ex5.
page 10
Geometry
Name: __________________________
Unit 6 – Similarity
Date: ___________________________
Example 6 – Find the missing side lengths and angle measures.
DABC ~ _________
Scale Factor:
Example 7 – Find the missing side lengths and angle measures.
page 11
Geometry
Name: __________________________
Unit 6 WS 7
Date: ___________________________
Determine whether the figures are similar. If so, name the similarity relationship and the scale factor.
Example
E
A
26
10
12
20
B
5
D
1.
70
15
B
6
13
E
F
6
D
15
10
C
F
Yes
4
10
C
24
A
H
G
4
Scale Factor: 2 to 1
DABC ~ DDEF
2. J
6
K
Q
5
P
3
8
R
6
M
L
65
6
H
55
125
115
4
7
T
A
G
T
18
80
A
80
110
27
75
C
110
D
G
165
80
55
R
12
8
F
21
B
165
6
E
115
14
T
6
125
12
I
80
W
20
U
5.
65
14
80
80
O
5
S
9
4
21
21
8
M
V
20
3
N
4.
3.
J
74
110
111
16
I
H
Geometry
Name: __________________________
Unit 6 WS 7
Date: ___________________________
In each problem the figures shown are similar. Name the similar figures; identify the scale
factor; find all missing side lengths and angle measures indicated by variables. Show work.
1.
z
35
18
21
85
D
T
Q
15
8
y
12
A
2.
F
B
60
P
C
18
15
S
E
x
x
z
y
80
U
R
14
y is a decimal.
Figures: ___________________________
Figures: ___________________________
Scale Factor: _______________________
Scale Factor: _______________________
x = ______
x = ______
3.
A
y = ______
16
z = ______
E
B
y
x
H
10
G
x
9
M
z = ______
N
z
12
15
D
4.
F
y = ______
60 O
z
Y
12
y
8
C
24
X
60
50
Z
16
x and y are decimals.
Figures: ___________________________
Figures: ___________________________
Scale Factor: _______________________
Scale Factor: _______________________
x = ______
x = ______
y = ______
z = ______
y = ______
z = ______
Geometry
Name: __________________________
Unit 6 WS 8
Date: ___________________________
In each problem the figures shown are similar. Name the similar figures; identify the scale
factor; find all missing side lengths and angle measures indicated by variables.
1.
A
2.
K
18
12
z
y
E
G
F
E
H
12
5
10
H
15
D
12
M
z
y
B
2.5
J
G
10
L
x
K
F
3
J
x
C
Figures: ___________________________
Figures: ___________________________
Scale Factor: _______________________
Scale Factor: _______________________
x = ______
x = ______
y = ______
3.
D
A
y
z = ______
E
4.
z
C
15
D
40
22
70
50
z = ______
B
30
12
F
y
110
x
15
A
y = ______
F
C
30
70
40
x
B
G
z
w
E
110
12
H
Figures: ___________________________
Figures: ___________________________
Scale Factor: _______________________
x = ______
y = ______
z = ______
Scale Factor: _______________________
w = _____ x = _____ y = _____ z = ____
What kind of quadrilaterals are these
figures? ___________________________