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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 ( ~ ): 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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