Similarity M7G3.a Understand the meaning of similarity, visually compare geometric figures...

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