3. $\triangle A B C$ and $\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$ are shown on the coordinate plane.
Devon claims that a sequence of rigid motions carries $\triangle A B C$ onto $\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$. Which actions could he take to prove his claim?
Answer
Final Answer: Devon could prove his claim by showing that the distances between corresponding points, the angles between corresponding sides, and the orientation of the triangles are the same.
Step 1 ：Show that the distance between each pair of corresponding points in the two triangles is the same. This would prove that the triangles are congruent, which is a necessary condition for one to be a rigid motion of the other.
Step 2 ：Show that the angles between each pair of corresponding sides in the two triangles are the same. This would prove that the triangles are similar, which is another necessary condition for one to be a rigid motion of the other.
Step 3 ：Show that the orientation of the triangles is the same. This means that if you move from point A to point B to point C in the first triangle, you would move from point A'' to point B'' to point C'' in the same order in the second triangle. This is necessary to prove that one triangle is a rigid motion of the other, and not just a reflection.
Step 4 ：Final Answer: Devon could prove his claim by showing that the distances between corresponding points, the angles between corresponding sides, and the orientation of the triangles are the same.
