Section Section 7.17.1

Ratio and ProportionRatio and Proportion

RATIOSRATIOSA comparison between A comparison between

numbers.numbers.

Simplifying RatiosSimplifying Ratios

Write the following ratios inWrite the following ratios in

simplest formsimplest form. .

a) 10:18 a) 10:18

b) b) 28

2

5:914

1

2 2

Geometric RatiosGeometric Ratios1)1)Find the ratio Find the ratio

of of AEAE to to BEBE..2)2)Find the ratio Find the ratio

of the largest of the largest angle of angle of ΔΔACEACE to the smallest to the smallest angle of angle of ΔΔDBEDBE..

3)3)Find the ratio Find the ratio of of angle Aangle A to to angle Dangle D..

5x

10

30

6060

30

E

A

B

D

C

10:5x

90o:30o3:1

2:x

60o:60o1:1

o

oo

o

Geometric RatiosGeometric Ratios

4)4)AB : BC AB : BC

5)5)AB : AB : perimeter of perimeter of ABCDABCD

6)6)

6

10

A B

D C

:m A m C

10:6

5:3 10:32

5:16 1:1

Triangles (SAT Triangles (SAT TYPE!)TYPE!)7)7)The measures of three The measures of three

angles of a triangle are in angles of a triangle are in the ratio of 2:2:5.the ratio of 2:2:5. Find Find the measures of each the measures of each angle. angle.

8)8)USE “x” anytime you have USE “x” anytime you have a ratio problem!!!!!!a ratio problem!!!!!!

2x, 2x, 5x

2x + 2x + 5x = 1809x = 180x = 20

2(20) = 40, 40, 5(20) = 100

Algebraic RatiosAlgebraic Ratios

If If x = 2x = 2 and and y = 3y = 3. . Write each ratio in Write each ratio in simplest form. simplest form.

9) 9) 6x6x22 toto 12xy 12xy 10) 10) 2

3

y x

x

6(2)2 to 12(2)(3)

24 to 721 to 3

2(3) 2

3(2)

4 2

6 3

Simplifying RatiosSimplifying Ratios

2611)

12

a

abc

1

2 2

a

bc

PROPORTIOPROPORTIONSNS1

2 4

x1· 4

= 2· x

4 = 2x2 = x

Simple Simple ProportionsProportions

4 812)

24y4· 24

= 8· y

96 = 8y 12 = y

Simple Simple ProportionsProportions

4 1113)

1x x

4· (x – 1) =

11· x4x - 4 =

11x-4/7 = x

- 4 = 7x

PRACTICEPRACTICE

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