7.2 Class Notes Ratio, Proportion, Similarity KEY

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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

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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

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

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Class Notes Date:

SIMILAR POLYGONS

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

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