Transcript Aim: What are Similar Polygons?

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
Download Sketch 48 and fill in the
accompanying worksheet.
Big Sara smiles
The lengths and widths of the
pictures are in the same ratio.
Little Sara smiles
~
Aim: Similarity
Similar corresponding,
comparable,
Course: Applied Geo.
alike
~
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
length A 10" 2


length B 5" 1
width A 4" 2


width B 2" 1
Similarly, find the ratio of the width of
picture A with the width of picture B
A
10”
The lengths and widths of the
pictures are in the same ratio.
~
B
corresponding,
5”
comparable,
Course: Applied Geo.
Aim: Similarity
4”
Similar -
alike
2”
~
Ratio
compares 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
other ratios equal to 1/4 are found by
multiplying numerator and denominator by the
same factor
Ex.
1 6 6
 
4 6 24
Reduce a ratio: divide numerator and
denominator by greatest common factor
Ex.
Aim: Similarity
6 6 1
 
24 6 4
Course: Applied Geo.
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
MEAN
EXTREME
1
3

2
6
MEAN
This proportion reads,
“1 is to 2 as 3 is to 6”
EXTREME
Cross Products: 1  6 = 2 


Property of Proportion
If two ratios form a proportion, then the
cross products are equal.
If the cross products of two ratios
are
Course:
Applied
Geo.
Aim: Similarity
equal, then the ratios form a proportion.
Are dimensions of corresponding parts for polygons
in column A & column B in the same ratio?
A
A
No
B
=
5
4
V
=
5 1

5 1
S
4 DC =
VU
4 1

4 1
DC
VU
B
AD
SV
5
C
A
Yes
=
5 1

5 1
5
D
5
D 4
AD
SV
C 3
S
B
T
5
4
U
T
5
V
4
U
HOW DO THE TWO PAIRS COMPARE?
Can you say either pair ofCourse: Applied Geo.
polygons is similar to each other?
Aim: Similarity
What does similar mean?
What does similarity mean in geometry?
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.
Aim: Similarity
Course: Applied Geo.
1. Similar polygons are two polygons in which the
A) corresponding sides are in proportion and the
B) corresponding angles are congruent.
A) Corresponding sides are in proportion
2
1
Ratio of Similitude
B) Corresponding angles are congruent
The scale factor comparing two corresponding sides of
similar polygons is also called the ratio of similitude
Aim: Similarity
Note:
Similar Polygons haveCourse:
theApplied Geo.
same shape, but are of different size
Quadrilateral 1 ~ Quadrilateral 2. Find the
value of the variables.
6
4
1
9
y
z
x
2
12
15
Recall: All corresponding sides of similar
polygons are in proportion:
the ratio of similitude or scale factor
What is the ratio of similitude for these
figures?
6 y

Aim: Similarity
9 12
y=8
6 4

9 x
x=6
6
9
6 z
 Course: Applied Geo.
9 15
z = 10