Transcript the size-change factor

WHAT WE HOPE YOU LEARN BY THE
END OF THIS PRESENTATION:
 What is a polygon?
 What are the different types of
polygons?
 What is a congruent polygon?
 What is a similar polygon?
 What are some examples of these
polygons?
A polygon is a plane having three or more
sides.
Convex polygon: all the sides are pushed
outward.
Concave polygon: at least two sides are
pushed inward.
Regular polygon: all the sides have the same
length and their angles are all the same size.
Take a minute to match the
name up with the figure . . .
fact:
Congruent polygons are polygons
that have the same size and the
same shape.
fact:
Congruent shapes have all their
sides and angles congruent.
Notice how the second
figures have the same shape
and size of the first – they
match exactly.
Now we are going to take a
look at similar polygons . . .
CAN YOU FIND THE SIMILAR
MATCHES?
Can you find similar polygons?
Same shape
(1) Triangle
(2) Rectangle
Different size
(3) Pentagon
(4) Hexagon
(5) Octagon
Angle does not change
Reduction
Enlargement
NOW, LET’S DEFINE
SIMILAR !!
Definition:
Figures that have exactly same shape
are called similar figures.
Properties:
(1) In polygons, the size of angles does not change.
(2) One figure is an enlargement or reduction of the
other.
(3) Congruent figures are similar because they gave
the same shape.
How can we know the length
of sides in similar figures?
If two figures are similar, one figure is an
enlargement of the other. The size-change
factor tells the amount of enlargement or
reduction.
Example 1: If a copy machine is used to copy a drawing or picture, the
copy will be similar to the original.
Original
Copy
Original
Copy
Original
Copy
Exact Copy
Enlargement
Reduction
Copy machine set to 100%
Copy machine is set to 200%
Copy machine is set to 50%
Size-change factor is 1X
Size-change factor is
2X
Size-change factor is 1 x
2
Example 2: The triangles CAT and DOG are similar. The larger
triangle is an enlargement of the smaller triangle. How long is
side GO?
T
G
2 cm
1.5 cm
? cm
A
3 cm
O
C
3 cm
6 cm
D
Each side and its enlargement
form a pair of sides called
corresponding sides.
(1) Corresponding side of TC -->
GD
(2) Corresponding side of CA-->
DO
(3) Corresponding side of TA-->
GO
Length of
corresponding
sides
GD=3
TC=1.5
DO=6
CA=3
GO=?
TA=2
Ratio of Lengths
3/1.5=2
6/3=2
?/2=2
The size-change factor is 2x.
G
? cm
T
2 cm
3 cm
1.5 cm
O
A
C
3 cm
D
6 cm
(1) Each side in the larger triangle is twice the size of
the corresponding side in the smaller triangle.
(2) Now, let’s find the length of side GO
i) What side is corresponding side of GO? TA
ii) What is the size-change factor? 2X
iii) Therefore, GO= size-change factor x TA
iv) So, GO= 2 x 2 = 4 cm
WHAT WE JUST LEARNED ABOUT
SIMILAR POLYGONS ?
Not change angle
Different size
Same shape
Similar polygons
Corresponding side
Size-change factor
Example 1: Quadrangles ABCD and EFGH are similar.
How long is side AD? How long is side GH?
(1) What is size-change factor?
12÷ 4= 3 & 18÷ 6=3
(2) What is corresponding side
of AD ? EH
(3) How long is side AD? AD = 5
H
15 cm
E
?cm
? cm
D
(4) What is corresponding side
of GH? CD
(5) How long is side GH? 7 x 3 = GH, GH = 21
A
12cm
7cm
4cm
C
B
6cm
F
18 cm
G
A polygon is a plane having three or more sides.
Congruent polygons are polygons that have
congruent
congruent
the same size
and the
same shape.
Similar polygons are polygons that have
the samesimilar
shape. similar
Circle Limit III
M.C. Escher
Similar figures look alike but one is a smaller
version of the other. Like Dr. Evil and Mini-Me.
It wouldn’t make much sense to make a drawing
of this ship the actual size of the ship.
Just like congruent polygons, the corresponding
angles in similar polygons must be congruent.
A = 80°
80°
W = ___
B = 30°
Z = 170°
30°
X = ___
D = ___170°
B
A
D
W
Z
C
X
Y
The sides are a little different.
They must be
PROPORTIONAL.
AB =
WX
XY
B
A
D
BC = CD = DA
YZ ZW
W
Z
C
X
Y
This means I should be able to multiply each side
of the smaller polygon by the same number and
get it’s corresponding side on the bigger polygon.
4x2 = 8
4
3x2 = 6
5x2 = 10
3
5
2
2x2 = 4
The SCALE FACTOR is the ratio
of the corresponding sides
or
SMALL
BIG
BIG
SMALL
What is the scale factor of these polygons?
10
4
6
X
7
Z
Y
8
Scale Factor
=
10 = 5
4
2
Use the scale factor to find the other sides
10
6
4
7
Z
X
Y
8
5 6
=
2 Z
5z = 12
z = 12 = 2.4
5
5 X
=
2 7
2x = 35
x = 35 = 17.5
2
SF =
10 = 5
4
2
5 =8
2 Y
5y = 16
y = 16 = 3.2
5