similar figures
Two figures are similar if one is a scaled copy of the other — the same shape, possibly a different size. Think of a photograph and an enlargement of it, or a model car and the real car. Every angle in the small figure matches the corresponding angle in the large one, and every length is stretched (or shrunk) by the same fixed multiplier. Nothing is bent, twisted, or stretched more in one direction than another.
Precisely, two polygons are similar when (1) their corresponding angles are equal, and (2) their corresponding sides are in proportion — all the side-ratios reduce to one common number called the scale factor. Both conditions are needed: a square and a non-square rectangle have all right angles but unequal side-ratios (not similar), while a square and a rhombus can have equal side-ratios but unequal angles (not similar). When figures are similar we write ABCD ~ A'B'C'D', and the order of the letters tells you which parts correspond. Congruent figures are the special case where the scale factor is exactly 1.
Similarity is what makes maps, blueprints, scale models, and photographic enlargement trustworthy: the shape is faithfully preserved even as the size changes. It is also the engine of indirect measurement — measuring a tall tree by its shadow, or a river's width by a sighting triangle — because corresponding parts of similar figures stay in proportion no matter how big the real thing is.
A 4-by-6 photo enlarged to 8-by-12 is similar: every angle is still 90 degrees and every length doubled, so the scale factor is 2. A 4-by-6 photo cropped to 4-by-4, however, is not similar to the original — the side-ratios changed.
Equal angles plus a common length-ratio is what 'same shape, different size' really means.
For triangles only, equal angles automatically force proportional sides (that is the AA criterion), so you can drop the side check. For four-or-more-sided figures you genuinely need both conditions — a counterexample like the square-versus-rhombus shows angles alone are not enough.