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 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 W X Y B P QR S

Proportions 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. x = 6

Example using a proportion M K L J SR QP x Quadrilateral JKLM is similar to quadrilateral PQRS. Find the value of x. x = 4

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