The statement "the corresponding angles of similar triangles are equal" is always true.
This is one of the fundamental properties of similar triangles. If two triangles are similar, then their corresponding angles are equal. This means that if we have two triangles that are similar, we can compare the angles of the two triangles by pairing up the corresponding angles and comparing them.
For example, if we have two similar triangles ABC and DEF, where angle A is corresponding to angle D, angle B is corresponding to angle E, and angle C is corresponding to angle F, then we know that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.
This property is also used in solving problems involving similar triangles, such as finding the lengths of sides or the measures of angles in one triangle given the corresponding measures in another similar triangle.