Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.
Use similar triangles to find a missing side or angle measure
Problem
Use triangle similarity to find \(x\): the scale factor from the smaller triangle to the larger triangle is \(3\), and a side of length \(5\) in the smaller triangle corresponds to \(x\) in the larger triangle.
A scale factor is directional, so the words smaller-to-larger control the operation. We’ll match the corresponding sides, apply the factor in its stated direction, evaluate the product, and divide the resulting pair in reverse to confirm that it reproduces the given scale.
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