Exercise 29. Prove: A rotation is an isometry and thus maps a preimage set to a congruent image set.
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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. The rotation $\triangle A^{\prime} B^{\prime} C^{\prime}$ is congruent to the preimage $\triangle A B C$.
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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 $\overline{A^{\prime} B^{\prime}}$ is a rotation of $\overline{A B},$ then $A B=A^{\prime} B^{\prime}$
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 point $C$ is between points $A$ and $B,$ then the rotation $C$ is between $A^{\prime}$ and $B^{\prime} .$
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