To identify the relationship between the preimage (original figure) and image (transformed figure) under the given transformations, we can classify each one as either congruent or similar:
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Rotation:
- Relationship: Congruent
- Explanation: Rotations preserve the shape and size of the figure, resulting in a congruent image.
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Translation:
- Relationship: Congruent
- Explanation: Translations move the figure without altering its shape or size, resulting in a congruent image.
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Dilation:
- Relationship: Similar
- Explanation: Dilations change the size of a figure while preserving its shape, resulting in a similar image (the angles remain the same, but the lengths of the sides change).
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Reflection:
- Relationship: Congruent
- Explanation: Reflections flip the figure over a line, preserving the shape and size, and thus resulting in a congruent image.
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Translation then Reflection:
- Relationship: Congruent
- Explanation: The combination of translation and reflection involves moves that maintain the shape and size of the figure, resulting in a congruent image.
So, to summarize the relationships:
- Rotation: Congruent
- Translation: Congruent
- Dilation: Similar
- Reflection: Congruent
- Translation then Reflection: Congruent