Question

1. show that the two triangles △abc∼△def are similar by comparing the ratios of the side lengths.

Explanation:

Step1: Calculate the ratios of corresponding sides

For side \(AB = 25\) and \(DE = 40\), the ratio is \(\frac{AB}{DE}=\frac{25}{40}=\frac{5}{8}\).
For side \(AC = 20\) and \(DF = 32\), the ratio is \(\frac{AC}{DF}=\frac{20}{32}=\frac{5}{8}\).
For side \(BC = 15\) and \(EF = 24\), the ratio is \(\frac{BC}{EF}=\frac{15}{24}=\frac{5}{8}\).

Answer:

Since \(\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}=\frac{5}{8}\), by the Side - Side - Side (SSS) similarity criterion, \(\triangle ABC\sim\triangle DEF\).