Use similarity transformations to decide similarity and explain angle equality and side proportionality in triangles.
Classify a transformation sequence by similarity invariants
Problem
A figure undergoes a dilation with scale factor \(2\) followed by a translation. Track angle preservation and length factors through \(\text{both}~\text{steps}\), state the composite uniform scale, and classify whether the sequence establishes similarity.
A transformation sequence is a similarity transformation when angles survive and every length receives one uniform composite factor. We’ll track those two invariants through the dilation, track them again through the rigid translation, multiply the stepwise length factors, and classify the final relationship from the combined result.
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