Identify similar polygons Use similarity to solve problems

1. Similar Polygons
The student is able to (I can):
• Identify similar polygons
• Use similarity to solve problems.

2. similarsimilarsimilarsimilar polygonspolygonspolygonspolygons – two polygons are similar if and only if their
corresponding angles are congruent and their
corresponding side lengths are proportional.
Example: Show that the two polygons are similar.
∠S ≅ ∠B
∠P ≅ ∠R
∠N ≅ ∠A
∠G ≅ ∠K
S P
NG
B R
AK
6
5
3
4
12
10
6
8
3 4 5 6
6 8 10 12
= = =
SPNG ~ BRAK

3. A similarity statementsimilarity statementsimilarity statementsimilarity statement describes two similar polygons
by listing their corresponding vertices.
Example: SPNG ~ BRAK
To check whether two ratios are equal, cross-multiply
them—the products should be equal.
Example:
3 4
6 8
=
24 24=

4. Example
Determine whether the rectangles are similar. If so, write
the similarity ratio and a similarity statement.
All of the angles are right angles, so all the angles are
congruent.
150 = 150 sim. ratio: QUAD ~ RECT
Q
U
A
D
R E
CT
15
6
25
10
6 15
?
10 25
=
3
5