Which of the following describes properties of similar triangles?

The properties of similar triangles state that all corresponding angles in similar triangles are congruent, not proportional, and the lengths of corresponding sides are proportional. In other words, if two triangles are similar, then the angles will have the same measure, while the ratios of the lengths of corresponding sides will remain constant.

In this context, the correct answer highlights the relationship between angles in similar triangles, affirming that angles correspond to one another in a consistent manner, which is essential in establishing similarity. Similar triangles can have different sizes; however, their angles will always be the same, solidifying the notion that angle measures are preserved even if the triangles' dimensions differ.

The other options do not accurately describe the properties of similar triangles. For instance, asserting that only one angle needs to be proven congruent does not align with the comprehensive definition of similarity, which requires that all corresponding angles are congruent. Claiming that the sides are equal in length is incorrect because while the sides of similar triangles have a consistent ratio, they are not necessarily equal unless the triangles are congruent. Lastly, stating that all angles are different contradicts the defining characteristic of similar triangles, which mandates that corresponding angles must be equal.