To accurately determine the type of transformation that maps ΔABC to ΔA′B′C′, I would need to see the image you are referring to. However, I can provide some general guidance.
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Reflection: This transformation flips the triangle over a line (the line of reflection). If the corresponding points of ΔA′B′C′ are mirror images of ΔABC across a line, then it is a reflection.
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Rotation: If ΔA′B′C′ is the same shape and size as ΔABC but is turned around a certain point (the center of rotation), then it is a rotation.
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No rigid transformation: This would apply if ΔA′B′C′ differs in size or shape from ΔABC, meaning there is no way to map it using only rigid transformations (reflection, rotation, or translation).
If you can describe the positions of the triangles or share any specific details about how they relate to each other (e.g., orientation, size, and correspondence of vertices), I might be able to help you deduce the correct answer more accurately!