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Similar polygons are often very useful in geometry. We call two polygons similar if all of their corresponding angles are equal, and all of their corresponding sides have the same ratio.
So, how can we say that two polygons are similar?
Try thinking about it a bit for polygons with fewer sides, like triangles. Once you think you have a general idea of how it works, continue.
The most common way of proving similarity is with angles. Two polygons are similar if and only if all of their corresponding angles are congruent. So, if two polygons with sides have congruent corresponding angles, the last pair of angles is also congruent and the polygons are similar to each other. This is especially powerful with triangles, where one must only show that two of the angles are congruent to conclude that two triangles are similar.
Another method of proving similarity is with the sides being in a common ratio. However, we would have to prove it for all pairs of corresponding sides. Again, we see that this method is most relevant with triangles, since usually we wouldn't be given enough information to determine that all pairs of corresponding sides are in the same ratio for other polygons.
We can also prove similarity using a combination of side length ratios and angles. Again, this is simplest to see with triangles: if two pairs of corresponding sides have equal ratios and their included angles are congruent, then the triangles are similar.
Notice that all regular polygons with the same number of sides are similar by default (congruent angles).