Use similarity transformations to decide similarity and explain angle equality and side proportionality in triangles.
Find the scale factor between similar triangles from a pair of corresponding sides
Problem
Triangles \(ABC\) and \(DEF\) are similar, and side \(AB\) corresponds to side \(DE\). Use \(AB=5\) and \(DE=15\) to find the scale factor from triangle \(ABC\) to triangle \(DEF\).
Big Picture
What this problem is really about
A similarity scale factor depends on both correspondence and transformation direction. We’ll decode the ordered triangle names to match the side pair, identify which triangle is the source and which is the target, divide target length by source length, and multiply forward to confirm the recovered factor reproduces the target side.
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