Question

1 practice 1 here are triangles abc and def. what is the length of segment df? type your answer in the box. units how did i do?

Explanation:

Step1: Determine similarity of triangles

Triangles \(ABC\) and \(DEF\) have two equal angles (\(68^{\circ}\) and \(44^{\circ}\)). By the AA (Angle - Angle) similarity criterion, \(\triangle ABC\sim\triangle DEF\).

Step2: Set up proportion for corresponding sides

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. \(\frac{AB}{DE}=\frac{AC}{DF}\). Given \(AB = 8\), \(DE=18\), \(AC = 6\). Let \(DF=x\). Then \(\frac{8}{18}=\frac{6}{x}\).

Step3: Solve the proportion

Cross - multiply: \(8x=18\times6\), so \(8x = 108\). Then \(x=\frac{108}{8}=\frac{27}{2}=13.5\).

Answer:

\(13.5\)