Bellwork Simplify

Solve

The area of a rectangle is 750 square meters. The ratio of the width to the length is 5:6. Find the width and length.

oz

lb

10

3

1

6

8

3

x

6

1

3

8 x

1

8

6

3

x

Clickers

Bellwork Solution

Simplify

oz

lb

10

3 3.1024

.5

.5

A

B

C

Bellwork Solution Solve

1

6

8

3

x

.15

.15.33

.45

A

B

C

Bellwork Solution Solve

6

1

3

8 x .15

.15.33

.45

A

B

C

Bellwork Solution

Solve

1

8

6

3

x .15

.15.33

.45

A

B

C

Bellwork Solution The area of a rectangle is 750 square meters. The ratio of

the width to the length is 5:6. Find the width and length.

.2.5

.5

.6

A

B

C

Use Proportions to Solve Geometry problems

Section 6.2

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

ReciprocityOnce concept that should be addressed before we continue is the concept of reciprocity

This is illustrated by the bellwork and can be further elucidated via this figure

These proportions are all similar statements. Why?

A C

B D

B D

A C

A B

C D

A B C D

B D

Reciprocity is the ability to rewrite proportions in different manners and achieve the same answer

Common Ratios• In the bellwork we talked about a ratio that exists between a

length and a width.

• Many times we also see a common ratio that exists between two objects

Let’s write the ratios that we see

3

4

5

A

B

C

5

3

BC

AB

5

4

BC

AC

4

3

AC

AB

Ratio ExampleThese triangles show a common ratio

Let’s now write the proportions that develop

3

4

5

A

B

C

AB BC

ED EF

AC BC

DF EF

AB AC

DE DF

Can we now use these relationships to solve for the unknown sides?

x

y

30

D

E

F

AB BC

DE EF

3 5

30x

AC BC

DF EF

4 5

30y

ExampleAssuming a similar ratio exists, find the measure of FE

A

B C

DE

FG

H

2

3

6

5

x+1

12

2y+2

.6.33

.7

.8

A

B

C

ExampleAssuming a similar ratio exists, solve for y

A

B C

DE

FG

H

2

3

6

5

x+1

12

2y+2

.11

.11.83

.24

A

B

C

Practical ExampleThe scale of a map is 1 in:1440 ft. Find the actual length of a street if the distance on the map is 3 inches.

.480

.1440

.4320

A ft

B ft

C ft

Homework

6.2 1-6, 8-18, 22-33, 38, 39

Practical ExampleA road gradient is measured in percentages, where a 100% grade is a 45o angle. Based on this information, what angle with the horizontal does a 40% grade make?

.10

.18

.40

.88

o

o

o

o

A

B

C

D

Most Important Points Using ratios in geometric relationships