What is true regarding the angles and sides of a congruent triangle?

The correct answer is that angles opposite congruent sides are congruent. This principle is a fundamental property of triangles and is a key part of the concept of congruence in geometry. When two triangles are congruent, it means that all corresponding angles and sides are equal in measure.

Therefore, if two sides of a triangle are equal in length, the angles opposite those sides must also be equal in measure. This relationship stems from the fact that congruent triangles maintain their shape and size, which implies that not only the sides but also the angles exhibit this correspondence.

This property is particularly useful in solving problems related to triangles, as it allows students to infer information about angles based on the lengths of sides and vice versa. Recognizing this congruence relationship helps in proving the congruence of triangles and understanding more complex geometric relationships.

The other options do not accurately describe the properties of congruent triangles. For example, the relationship between the angle measures and the side lengths is more nuanced than stated in other choices, and they do not align with established geometric principles.