Transcript Scale Factor

Geometry 6.3
Big Idea: Use Similar
Polygons
Similar Polygons: Two
polygons where corresponding
angles are congruent and
corresponding side lengths
are proportional (not
congruent)
Symbol for similarity is ~
Scale Factor: In two similar
polygons, the ratio of the
lengths of two corresponding
sides. All corresponding sides
have the same ratio for
similar polygons.
Theorem 6.1 Perimeters of
Similar Polygons
If two polygons are similar,
then the ratio of their
perimeters is equal to the
ratios of their
corresponding sides
(scale factor).
Example: In the diagram, DRST » DXYZ
1)
2)
List all pairs of congruent angles.
Check that the ratios of
corresponding sides lengths are
equal.
T
25
R
3)
Write ratios of the corresponding
side lengths in a statement of
proportionality.
1)
What is the scale factor?
2)
What is the ratio of the perimeters?
Z
30
20
15
S
18
X 12 Y
1.
Are these
triangles similar?
1.
If yes, what is the
scale factor?
2.
What is the ratio
of the
perimeters?
Example: In the diagram, DDEF » DMNP
N
E
Find the value of x.
12
20
M 16
9
P
x
D 12 F
In the diagram, ABCD » QRST
1. Find the value of x.
12
10
B
x Q 6 R
D
16
C5
A
2. What is the scale factor
of QRST to ABCD?
T
4
8
S