Identify corresponding parts of similar polygons, compute the scale factor, and use it to find unknown sides and perimeters.
Two polygons are similar when two conditions both hold: every pair of corresponding angles is congruent, AND every pair of corresponding sides is proportional, all with the SAME scale factor (the ratio of similarity). We write triangle ABC ~ triangle DEF for "triangle ABC is similar to triangle DEF" -- using ~ instead of the usual similarity symbol, a stand-in the same way ~= stands in for congruence. Just like with congruence statements, letter order in a similarity statement shows the correspondence.
Similar figures are exactly what a dilation produces: stretch or shrink a figure from a center point, and the image is always similar to the original, whether or not a rigid motion is layered on top to reposition it. One easy consequence is worth remembering: if two similar figures have scale factor k, their PERIMETERS also have ratio k, since a perimeter is just a sum of sides and every side scaled by the same k. (Areas behave differently -- they scale by k^2 -- a fact we will use once we reach area.)
Mastery looks like: They correctly identify corresponding parts from a similarity statement, compute the scale factor between similar figures, and use it to find unknown side lengths or perimeters.
Common stumbles: Setting up the scale factor upside down (mixing up which figure is on top); assuming any two figures with the same shape name are automatically similar without checking the side ratios match.