1. Let's start by stating the problem: We want to understand how to use similarity in triangles to solve problems. 2. Similar triangles have the same angles and their corresponding sides are in proportion. 3. If two triangles \(\triangle ABC\) and \(\triangle DEF\) are similar, then: $$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$$ 4. To solve problems, identify pairs of similar triangles by their angles. 5. Use the side length ratios from the similar triangles to find unknown lengths. 6. For example, if \(\triangle ABC \sim \triangle DEF\) and you know \(AB = 3\), \(DE = 6\), and \(BC = 4\), find \(EF\): $$\frac{AB}{DE} = \frac{3}{6} = \frac{1}{2}$$ Therefore, $$\frac{BC}{EF} = \frac{1}{2} \implies EF = 2 \times BC = 2 \times 4 = 8$$ 7. This step-by-step process helps you solve for unknown sides using similarity. Final answer: Use angle similarity to set up proportional sides and solve for unknowns.