As we have seen, translations, rotations, and reflections are isometries: pre-images and images are congruent. Dilation is a transformation that is not an isometry. The pre-image and image are similar, not congruent.

Two figures are similar when they have the same shape but not necessarily the same size.  Quadrilaterals ABCD and EFGH have the same shape but are clearly different sizes.  The two quadrilaterals below are similar.  Similar figures are symbolized:   


Similar Polygons

In more specific terms, the corresponding angles of similar figures are congruent and the corresponding sides have a common ratio.  In the figures above, angle A corresponds to angle E and therefore is congruent.  Because of this fact, when writing similarity statements the order of the letters in the pre-image needs to match their corresponding angles in the image.