9.1 Properties of Similar Figures
Proportion—an equation which shows that two ratios are equal.
The proportion a = c
and a:b = c:d.
b d
It is read “a is to b as c is to d.
Similar Figures—Two figures are similar if these two conditions are
true:
1. Corresponding angles are congruent
2. The lengths of corresponding sides are in proportion
The symbol ~ means “is similar to”
Remember—when you write a proportion, the ratios must compare
corresponding lengths.
Examples of Similar Figures

The trapezoids shown below are similar; they have the same shape but they are different in
size.
More about Similar Figures
Any two corresponding sides in two similar figures have a common ratio called the scale factor.
The trapezoids ABCD and EFGH shown above are similar. So,
.