Course: Applied Geo.Aim: Similarity

Aim: What are Similar Polygons? What is a Scale Factor or Ratio of Similitude?

Do Now: What is ratio of the length of picture A to the length of picture B

Big Sara smiles

Little Sara smiles

The lengths and widths of the pictures are in the same ratio.

Similar -

corresponding,

comparable,

alike ~

~

Download Sketch 48 and fill in the accompanying worksheet.

Course: Applied Geo.Aim: Similarity

Aim: What are Similar Polygons? What is a Scale Factor or Ratio of Similitude?

Do Now: What is ratio of the length of picture A to the length of picture B

10”

5”

2”4”

Similarly, find the ratio of the width of picture A with the width of picture B

Blength

Alength

1

2

"5

"10

A

B

Bwidth

Awidth

1

2

"2

"4

The lengths and widths of the pictures are in the same ratio.

Similar -

corresponding,

comparable,

alike ~

~

Course: Applied Geo.Aim: Similarity

Ratiocompares 2 numbers by division

the ratio 1 to 4 is written 1 : 4 or 1/4 the ratio 4 : 1 is not the same as 1 : 4

Reduce a ratio: divide numerator and denominator by greatest common factor

Ex.

4

1

6

6

24

6

other ratios equal to 1/4 are found by multiplying numerator and denominator by

the same factor

Ex. 24

6

6

6

4

1

Course: Applied Geo.Aim: Similarity

Proportion An equation that says two ratios are

equivalent (equal).

In a proportion, the product of the means is equal to

the product of the extremes

Proportion An equation that says two ratios are

equivalent (equal).

In a proportion, the product of the means is equal to

the product of the extremes

Property of Proportion If two ratios form a proportion, then the

cross products are equal. If the cross products of two ratios are equal, then the ratios form a proportion.

6

3

2

1

EXTREME

EXTREME MEAN

MEAN

This proportion reads, “1 is to 2 as 3 is to 6”

1 6 = 2 Cross Products:

Course: Applied Geo.Aim: Similarity

A B

5 5

5 4

1

1

5

5

4

5

4 4

55

No

Yes

Can you say either pair of polygons is similar to each other?

Can you say either pair of polygons is similar to each other?

ADSV =A B

CD

S T

UV

DCVU =

A B

CD

S T

UV

Are dimensions of corresponding parts for polygons in column A & column B in the same ratio?

ADSV =

DCVU =

HOW DO THE TWO PAIRS COMPARE?

4

31

1

4

4

1

1

5

5

Course: Applied Geo.Aim: Similarity

How do we define precisely what are properties of similar figures?

•Are corresponding parts congruent?

•Are corresponding angles congruent?

•Do the shapes look alike?

•Can they look different?

Explain what you think is meant by similar geometric shapes.

What does similar mean?

What does similarity mean in geometry?

Course: Applied Geo.Aim: Similarity

1. Similar polygons are two polygons in which the A) corresponding sides are in proportion and the B) corresponding angles are congruent.

The scale factorscale factor comparing two corresponding sides of similar polygons is also called the ratio of similituderatio of similitude

The scale factorscale factor comparing two corresponding sides of similar polygons is also called the ratio of similituderatio of similitude

A) Corresponding sides are in proportion

B) Corresponding angles are congruent

1

2

Ratio of Similitude

Note: Similar Polygons have the same shape, but are of different size

Note: Similar Polygons have the same shape, but are of different size

Course: Applied Geo.Aim: Similarity

What is the ratio of similitude for these figures?

Quadrilateral 1 ~ Quadrilateral 2. Find the value of the variables.

6

4x

y

z15

129

Recall: All corresponding sides of similar polygons are in proportion:

the ratio of similitude or scale factor

9

6

129

6 y

x

4

9

6

159

6 z

y = 8 x = 6 z = 10

12