A ratio is a comparison of two numbers such as 4:5. When writing a ratio, always express it in simplest form. A B C D What is the ratio of segment AB to segment CB? AB CB = 10 6 Now try to reduce the fraction. Once reduced this is the ratio between the two sides = 5353 Therefore, the ratio of segment AB to segment CB is 5:3.

Proportion: an equation that states that two ratios are equal. abab = cdcd Ratio Proportion

x6x6 = x = 6 5 8x = x = 3.75 Solving a proportion: Example

Formal Definition of Similar Polygons Two polygons are similar iff their corresponding angles are congruent,and (lengths of) corresponding sides are proportional. C A B E D F 1.  A   D 2.  B   E 3.  C   F

The ratio of corresponding sides of similar polygons. Example The scale factor  from  ABC to  _____ is____.  from  ZYX to  ABC is____. Scale Factor C A B Z Y X ZYX 2 1/2

Naming Similar Polygons **Must match the corresponding letters**

Applying the Definition - Angles **Must match the corresponding vertices**

Applying the Definition - Sides **Must match the corresponding sides** Proportional means all of the ratios are equal!

Example 3 ABCD  EFGH. Solve for x, y and z. 5 z x 10 y B C A D F G E H x = 7.5 Step 1: Write a proportion using names of sides. Step 2: Substitute values. Step 3: Cross-multiply to solve. Step 4: Repeat to find other values. y = 10z = 15