This document discusses identifying and using similar polygons. It defines similar polygons as two polygons where corresponding angles are congruent and corresponding side lengths are proportional. It provides an example of showing two polygons are similar by listing equal corresponding angles and equal ratios of corresponding sides. The document explains a similarity statement lists the corresponding vertices of similar polygons and gives an example similarity statement. It also describes how to check if two ratios are equal by cross-multiplying. An example problem is included to determine if two rectangles are similar by checking if corresponding angles are congruent and sides are proportional.

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