Similar figures and congruent figures both
have the same shape. The difference between similar figures and congruent
figures is that congruent figures also have the same size. So,
corresponding sides and corresponding angles of congruent figures have
the same measures. The measures of corresponding angles in similar figures are
the same, but the measures of corresponding sides in similar figures are
multiples of each other (i.e., they are proportional). Therefore, in order to
prove that any two figures are similar, one must show that these two conditions
hold for all corresponding angles and all corresponding sides of the two
figures.
For example, the two parallelograms below are similar figures.
Notice that they have the same shape, but obviously not the same size. All four
of their corresponding angles are congruent, and all four of their corresponding
sides are proportional (here, in a ratio of 1 to 2, or 0.500).
