Use similarity transformations to establish the AA similarity criterion.
Use AA similarity to find a missing side
Problem
The triangles are similar by \(AA\). Use this information to find the missing side: corresponding sides \(4\) and \(12\) match, and \(5\) corresponds to \(x\).
AA establishes that corresponding sides are proportional; it does not make their lengths equal. We’ll use the angle evidence to justify similarity, confirm the two stated side pairings, compute the target-to-source factor from the fully known pair, apply it to the unknown pair, and verify equal ratios.
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