What characteristic defines similar triangles?

Similar triangles are defined by two key characteristics: their corresponding angles are equal, and their corresponding sides are proportional.

When two triangles are similar, one triangle can be thought of as a scaled version of the other. The equality of corresponding angles ensures that the triangles have the same shape, while the proportionality of their corresponding sides indicates that the size may differ but the ratio between all pairs of sides remains constant.

This combination of equal angles and proportional sides is essential in proving the similarity of triangles in geometric contexts. For example, if you know that two triangles have two pairs of corresponding angles that are equal, you can conclude that the triangles are similar, which then implies that their sides will maintain a consistent ratio relative to one another.

By confirming both of these conditions, one can confidently assert that the triangles in question are similar, making the correct answer a combination of the characteristics defined in the choices.