SIMILARITY April 25, 2008

Brief Review

Medians  What is a median?

Altitudes  What is an altitude?

Perpendicular bisector  What is perpendicular bisector?

Angle bisectors  What is an angle bisector?

All About Ratios

What is a ratio?  The ratio of one number to another is the quotient when the first number is divided by the second.  Like this: ½  What is another name for a ratio?

Writing ratios in their simplest form  Find common factors.  Divide the numerator and denominator by any common factors.  Try these:

Extended Ratios  This form can be used to compare three or more numbers as well. This sort of ratio is known as an extended ratio. For example, the ratio a : b : c (read "a to b to c") means  The ratio of the first two numbers is a : b.  The ratio of the last two numbers is b : c.  The ratio of the first and last number is a : c.

Using extended ratios  The measures of the three angles of a triangle are in the ratio 2 : 3 : 4. Find the measure of each angle.

All about proportions

What is a proportion?  A proportion is an equation stating that two ratios are equal.  For example:  A:B = C:D

What is an extended proportion?  When three or more ratios are equal, you can write an extended proportion.

How do you solve a proportion?  Look at this problem. How would you solve it?

Properties of proportions  All of the following are equivalent to Why? AD=CB

All about similarity

What does it mean to be similar?  Two polygons are similar if their vertices can be paired in such a way that:  Corresponding angles are congruent.  Corresponding sides are in proportion (their lengths have the same ratio).  The ratio of the lengths of two corresponding sides is called the similarity ratio or (scale factor) of the similarity.

Finding ratios for corresponding parts  Examine the corresponding sides and determine the scale factor using a ratio.  Polygon ABCDE ~ polygon STUVW

What if the polygons overlap?  Check these triangles.