For two polygons to be similar, what must be true about their corresponding sides?

For two polygons to be classified as similar, their corresponding sides must be proportional in length. This means that the ratios of the lengths of corresponding sides of the two polygons must be equal. If one polygon's sides are scaled up or down by a certain factor compared to the other, they maintain the same shape but differ in size. This proportionality allows the overall geometric figures to have the same angles, making them similar.

If the sides of the polygons were only congruent, they would be identical in size, thus negating the concept of similarity. Inversely proportional lengths wouldn’t satisfy the requirements for similarity either, as that implies a specific type of relationship not applicable to scaling. Additionally, having sides that vary greatly would disrupt the necessary proportional relationships required for the polygons to be similar. Therefore, the correct condition for two polygons to be similar is that their corresponding sides must indeed be proportional.