Transcript Example 1 – Similar Polygons

SIMILAR POLYGONS
• Identify similar figures
• Solve problems involving scale factors
Ford Model A (?)
IDENTIFY SIMILAR FIGURES
When two polygons have the same shape but may be
different in size, they are called similar polygons,
Key Concept
Similar Polygons
Two polygons are similar if and only if their
corresponding angles are congruent and the measures
of their corresponding sides are proportional
D
H
10
5
8
4
E
A
5
B
6
C
2.5
F
3
G
The order of the vertices in a similarity statement is
important. It identifies the corresponding angles and the
corresponding sides.
D
H
10
5
8
4
E
A
5
B
6
C
2.5
F
ABCD ~ EFGH
3
G
Example 1 – Similar Polygons
Determine whether the figures are similar. Justify your
answer.
F
B
12
6
A
4.5√3
4.5
30°
E
30°
C
9
6√3
• All right angles are congruent, so C  F
• Since mA  mD, A  D
• By the third angle theorem, B  E
D
Example 1 – Similar Polygons continued
Determine whether the figures are similar. Justify your
answer.
F
B
12
6
A
4.5√3
4.5
30°
E
30°
C
D
9
6√3
Now, let’s determine if corresponding sides are proportional.
AB 12
  1.3
DE 9
BC 6

 1.3
EF 4.5
AC
6 3

 1.3
DF 4.5 3
SCALE FACTORS
When you compare the lengths of corresponding
sides of similar figures, you usually get a numerical
ratio.
This ratio is called the scale factor.
Example 2 – Scale Factor
Some special effects in movies are created using
miniature models. In a recent movie, a model sportsutility vehicle (SUV) 22 inches long was created to look
like the real 14⅔-foot (176 inch) SUV. What is the scale
factor of the model compared to the real SUV?
length of the model
22 inches

length of the real SUV 176 inches
1

8
Volvo XC90
Example 3 – Proportional Parts and Scale Factor
A
R
B
S
x
V
To find x:
18
ST VR

BC EA
18 x

4 3
18(3)  4( x)
54  4( x)
13.5  x
T
3
E
4
C
U
(y + 2)
5
D
Example 3 – Proportional Parts and Scale Factor cont.
A
R
B
S
x
To find y:
V
18
ST TU

BC CD
18 y  2

4
5
18(5)  4( y  2)
90  4 y  8
82  4 y
20.5  y
T
3
E
4
C
U
(y + 2)
5
D
Example 4 – Scale Factors on Maps