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For two triangles to be similar, they must have proportional corresponding sides. This means that the lengths of their sides must be in the same ratio, even if the actual lengths are different. Similar triangles have the same shape but may differ in size. This proportional relationship ensures that the angles in both triangles are also equal, leading to the conclusion that their geometric properties—such as angles and side ratios—are consistent across the two triangles.

Having the same area is not a requirement for similarity, as two triangles can have the same area but different shapes and sizes. Similarly, being right triangles is not necessary for similarity; triangles can be similar regardless of their types (right, acute, or obtuse). Lastly, having the same perimeter does not guarantee similarity; two triangles can have identical perimeters but different shapes and proportions. Thus, the critical requirement for similarity between two triangles is the proportionality of their corresponding sides.