Transcript similar polygons

WARM-UP
x = 18
t = 3, -7
u = ±7
7-2 Similar Polygons
I CAN
•Use the definition of similar polygons to
determine if two polygons are similar
•Determine the similarity ratio between two
polygons.
•Create a similar figure using a similarity
ratio
Figures that are similar (~) have the same shape
but not necessarily the same size.
Two polygons are
similar polygons if
and only if their
corresponding angles
are congruent and their
corresponding side
lengths are
proportional.
Review Congruent Triangles  Does
AAA prove triangles are congruent?
What would AAA prove?
Two polygons are similar if and only if:
1. ALL corresponding angles are congruent
2. ALL corresponding sides are proportional.
Is
PQR similar to
ZYX ?
Y
Q
15
9
P
R
18
Are corresponding angles equal?
<Q<Y
<P<Z
}
Given
< R  < X 3rd Angle Theorem
YES
6
10
X
Z
12
Are ratios of corresponding sides equal?
PQ = 9 = 3
ZY
6
2
RQ = 15 = 3
YX
10
2
PR = 18 = 3
ZX
12
2
YES
A similarity ratio is the ratio of the lengths of
the corresponding sides of two similar polygons.
The similarity ratio of ∆ABC to ∆DEF is
, or
The similarity ratio of ∆DEF to ∆ABC is
, or 2.
.
How is the similarity ratio and scale factor related?
The similarity ratio is the reciprocal of the scale factor!
Similarity Statement
PQR ~
ZYX
“is similar to”
Y
Q
15
9
P
R
18
6
10
X
12
The similarity ratio of triangle PQR to triangle ZYX is 9 to 6
or 9 = 3
6
2
The similarity ratio of triangle ZYX to triangle PQR is 6 to 9
or 6 = 2
9
3
Z
Example
Is
ABC similar to
KLJ ?
10
K
B
18
8
2
J
4
A
C
5
L
Are corresponding angles equal?
<A<K
<B<L
}
Given
< C  < J 3rd Angle Theorem
YES
Are ratios of corresponding sides equal?
AB = 2 = 1
KL
4
2
BC = 8 = 4
JL
18
9
NO, the sides are not proportional!
Writing Math
Writing a similarity statement is like writing a
congruence statement—be sure to list
corresponding vertices in the same order.
Application Problem
You are building a model of the school. The similarity
ratio of the model to the actual building is 1
400
If the actual building is 1,000 ft wide, how wide is the
model?
Model = 1
400
Actual
=
x
1,000
x = 2.5 feet wide
Your Turn
The ratio of a model scale die cast motorcycle is 1:18.
The model is 5 ¼ inches long. What is the length of the
actual motorcycle in feet and inches?
7 ft 10 ½ in