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Two polygons are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. Similarity is a mathematicians way of saying "expanded" and "shrunk". Two figures are "similar" if one is a shrunk down version of another. You can see this in the image below. The triangles all have the same shape but different sizes.

similar triangles

If two polygons, say ABCD and WXYZ are similar then this is written ABCDis similar toWXYZ. The order of the letters is important. They need to be sorted so that the corresponding angles are in the same position in each list. In other words if we say ABCDis similar toWXYZ then we must have Ais congruent toW, Bis congruent toW, etc.

You can also get the proportional sides from the order of the letters. Using ABCDis similar toWXYZ we would have: