Once you have proved that the rotation image of a segment is congruent to the preimage, how could you prove the following? Write a plan for each proof.
If $\angle A^{\prime} B^{\prime} C^{\prime}$ is a rotation of $\angle A B C,$ then $\mathrm{m} \angle A B C=\mathrm{m} \angle A^{\prime} B^{\prime} C$.