Similarity

M7G3.a Understand the meaning of similarity, visually compare

geometric figures similarity, and describe similarities by listing

corresponding parts.

What is Similarity?

Not Similar

Similar

Similar

Not Similar

Ratios

A ratio is a way to compare two numbers. The ratio of x to y can be written in three ways:

x to y, x:y, x/y

Ratios are expressed in simplified form:The ratio of 6:8 is simplified to 3:4

Ratios that have different units of measure, must be converted to like units before they are simplified.

A

C

B

F

ED

3 inches

8 inches

The ratios of the sides lengths of DEF to the corresponding sides lengths of ABC are 2:1. Find the unknown lengths

DF= AB=

Similar Figures

Similar Polygons

Similarity between two polygons: symbol is ~• Corresponding angles are equal (marked with arcs)

• Lengths of the sides of the polygon are proportional

List all of the pairs of the equal

(congruent ) angles.

Similar Polygons

What is the measure of angle b?

List the ratio of side lengths:

 

is called the scale factor

What is the scale factor?• Since these two polynomials are similar,

calculate the scale factor.

10 15

4 6

W

X Y

B

P

Q R

S

Proportions

10

415x

A proportion is an equation stating that two ratios (written as fractions) are equal.

You can check to see if two ratios form a proportion using their cross product.

Since we know that cross products work for proportions, we can use them to solve for a variable.

10

15

4x

x = 6

Example using a proportion

15

6

10

x

M

K

L

J

SR

Q P10

156

x

Quadrilateral JKLM is similar to quadrilateral PQRS. Find the value of x.

15

106 x x = 4

3.5

5

16

x

Real Life Application:Photographic Enlargements

You have been asked to create a poster to advertise a CD for Chris Brown You have a 4 inch by 5 inch photo for you to enlarge. You want the enlargement to be 16 inches wide. How long will it be?

4

16