What characterizes similar triangles?

Similar triangles are characterized by having angles that are congruent and sides that are proportional. This means that when two triangles are similar, their corresponding angles are equal in measure, which is a key feature of similar figures. Additionally, the lengths of their corresponding sides maintain a consistent ratio, known as the scale factor.

This proportionality of sides ensures that while the triangles may differ in size, their shapes remain the same. For example, if one triangle has sides of lengths 3, 4, and 5, and another triangle has sides of lengths 6, 8, and 10, they are similar because the ratios of the sides (3:6, 4:8, and 5:10) are all consistent.

In contrast, the other options do not adequately describe similar triangles. All sides being equal pertains to congruent triangles rather than similar ones. Having the same area is not a characteristic of similar triangles since they can have different areas depending on their size. Lastly, the presence or absence of right angles does not determine similarity; triangles can be similar regardless of their angles being acute or obtuse. Thus, the defining features of similar triangles rest on their congruent angles and proportional sides.