Bellwork

A stack of 100 nickels is 6.25 inches high. To the nearest cent, how much would a stack of nickels 8 feet high be worth?

Clickers

BellworkA stack of 100 nickels is 6.25 inches high. To the nearest cent,

how much would a stack of nickels 8 feet high be worth?

100 12 8 $.05

6.25 1 1 1

N in ft

in ft N

$76.80

Use Similar Polygons

Section 6.3

The Concept Yesterday we reviewed ratios and proportions and also talked

about the relationship between two objects Now we’re going to suffuse the two concepts into a practical

application of similar polygons

Scale Factor• Scale factor is the scalar multiplier used to relate similar

objects• Scale factor is typically used when discussing maps,

blueprints or even models of buildings or cars

Important PointsWhen we talk about scale factor it is important to be cognizant of

two important points

1. Scale factor is found through the ratio of the second object to the first

2. “Scaling” a polygon only effects the side length, not the angle measure

1

4

65

2

60o

1210

12 2

6 1 Scale factor of 2

30o

60o

30o

5 10

8

ExampleWhat’s the scale factor between these two objects?

8

1210

4235

28

..286

.3.5

.7

A

B

C

ExampleWhat’s the scale factor between these two objects?

2014

166

10 7

83

..5

.2

.4

A

B

C

ExampleThe object on the left is scaled by a factor of 4.75. What is the

length of the corresponding side to AB of the new figure?

15 11

16

19

.4

.71.25

.76

.90.25

A

B

C

D

A

B

C

D

TerminologyWhen two objects are scaled, they are considered similar objects

SimilarityThe relationship between two or more two dimensional

figures via a common ratio

In fact, we can explain congruence as a similarity with a common ratio of 1This can be seen in the notation for similarity vs. congruence

And by the fact that we utilize similar jargon, such as corresponding parts

~

Congruence

Similar

ExampleWrite the similarity statement for these two objects?

A

. ~

. ~

. ~

. ~

A ABD ACD

B CAE CBD

C ACE DCB

D EDC ABCB

C

D

E

Further RelationshipsWhat’s the ratio between these two triangles?

6

8

10

A

B

C

2

3

6

9

AB

DE

Does this ratio hold true for perimeters

9

12

15

D

E

F

2

3

24

36

8106

12159

ABC

DEF

P

P

Perimeter Theorem

Theorem 6.1: Perimeters of Similar PolygonsIf two polygons are similar, then the ratio of their perimeters is

equal to the ratios of their corresponding side lengths

ExampleWhat’s the perimeter of object 2?

2214

188 4

.11

.31

.62

A

B

C

ExampleWhat’s the perimeter of object 2?

15 11

16

19

.1.375

.26.125

.61

.83.875

A

B

C

D

Object 222

Practical ExampleYou are constructing a rectangular play area. You are basing your dimensions on a similar playground that has a length of 25m and a width of 15m. Your play area will only be 10m in length. How much fencing will you have to buy for your new play area?

.2.5

.32

.80

.150

A m

B m

C m

D m

AnalysisBilly Joe has a rectangular pasture with a perimeter of 1500ft. He likes to show off his mathematical abilities to his friends Daryl and Darrell, by explaining that his pole barn is exactly 20% the size of his pasture. What is the perimeter of his pole barn?

.150

.300

.1234

.30000

A ft

B ft

C ft

D ft

Unfortunately, a new survey was done on Billy Joe’s land and showed that the cornerstone had moved and his property line was actually 25 feet in on one of the sides (the whole line moved). Can he still make the claim about his pole barn?

. , '

. ,

. , '

. ,

AYes his barndidn t change

B No the ratioof thetwochanged

C No the perimeter won t change

D Yes polebarnsarechangeable

Homework

6.3 1-8, 9-27 odd, 30-32

ExampleFind the missing dimensions• ΔABC~ΔDEF• ΔABC is equilateral

A

B

CE

D F

10

10

10

.5

.10

.20

DF

A

B

C

.5

.10

.20

AC

A

B

C

Most Important Points Using ratios in geometric relationships