December 06, 2016
Unit 5, Lesson 5
Similar Polygons
"All cases are unique and very similar to others."
-T. S. Eliot
Similar Figures
- Figures with the same shape, but not
necessarily the same size.
December 06, 2016
Definition of Similar Figures
Two polygons are similar if and only if their vertices can be paired such that:
(1) Corresponding angles are congruent
(2) Corresponding sides are in proportion
(their lengths have the same ratio)
The symbol for similarity is ~
Example 1: GivenΔABC and ΔDEF, write a similarity statement.
December 06, 2016
Similarity holds with the following properties:
1. Reflexive
2. Transitive
3. Symmetric
A scale factor is the ratio between corresponding
side lengths of similar polygons
What is the scale factor of example 1?
December 06, 2016
A convenient way to label corresponding vertices is:
A and A' (read A prime); B and B' ; and so forth
This makes it easier to see all the corresponding sides and angles.
Example 2:
b) the scale factor of quad MANY to quad M'A'N'Y' is_________
c) NA = _____
N'Y' = _____
M'Y' =_____
d) the ratio of the perimeters is _________
December 06, 2016
Example 3: ΔXYZ ~ ΔMNO. Find the values of the variables.
Example 4: ΔABC ~ ΔADB, AC = 4 and AD = 9. What is AB?
December 06, 2016
Example 5: Given: ΔABC ~ ΔSTR
Are all isosceles triangles similar? why?
Are all right triangles similar?
Are all squares similar?
December 06, 2016