Download the size-change factor

Congruent figures are the same
shape AND size.
A: The same shape, but different
sizes?
B: Different shapes, but the same
size?
Are these figures:
•Congruent
•Similar but not congruent
•Neither
The figures are similar because they
are the same shape, but not the
same size.
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 factor1X
is
Size-change factor2X
is
Size-change factor1isx
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
Not change angle
Different size
Same shape
Similar polygons
Corresponding side
Size-change factor
Two angles whose
measure add up
to 90°.
45°
45°
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
EH of AD ?
(3) How long is side AD? AD = 5
H
15 cm
E
?cm
? cm
D
12cm
(4) What is corresponding side
CD of GH?
(5) How long is side GH? 7 x 3 = GH, GH = 21
A
7cm
4cm
B
C
6cm
F
18 cm
G
Two angles
whose
measures add up
to 180°.
90°
90°
When a transversal
intersects two parallel
lines, eight angles are
formed.
1. 2
3. . 4.
5.
7.
6.
8.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 3 and Angle
6 are congruent
angles. This means
they have the same
measure.
1.
2
3. . 4.
5.
6.
7. 8.
Angle 4 and
Angle 5 are
congruent
angles.
The measure of angle 4 and the
measure of angle 6 are congruent
AND
The measure of angle 3 and the
measure of angle 5 are congruent.
Alternate Interior
Angles are on
“alternate” sides
and on the
“interior” of the
parallel lines.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 1 and Angle 4
are congruent
angles.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 2 and Angle 3
are congruent
angles.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 5 and Angle 8
are congruent
angles.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 6 and Angle 7
are congruent
angles.
The measures of Angle 1 and Angle 3 are
congruent.
The measures of Angle 2 and Angle 4 are
congruent.
The measures of Angle 5 and Angle 7 are
congruent.
The measures of Angle 6 and Angle 8 are
congruent.
Vertical Angles are
diagonally across
from each other.
These angles are a bit trickier. You
have to imagine cutting your
diagram apart, and then pasting
one part on top of the other.
1. 2
3. . 4.
5. 6.
7. 8.
Angle 1 and Angle 5
are congruent
angels.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 2 and
Angle 6 are
congruent.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 3 and Angle 7
are congruent angles.
1.
2
3. . 4.
5. 6.
7. 8.
Angle 4 and
Angle 8 are
congruent
angles.
Angle 1 and Angle 5 are congruent.
Angle 2 and Angle 6 are congruent.
Angle 3 and Angle 7 are congruent.
Angle 4 and Angle 8 are congruent.
Now that you’ve seen what is
congruent, you can take the
measurement of “1” angle and figure
out the others. Let’s try it!
Angle 2 measures 110°. What
do the other angles measure?
1.
2
3. . 4.
5. 6.
7. 8.