Question

determine if triangle def and triangle ghi are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Calculate the ratios of corresponding sides

For \(\triangle DEF\) and \(\triangle GHI\), assume the correspondence \(DE = 18\), \(EF=24\), \(FD = 28\) and \(GH = 45\), \(HI = 60\), \(IG=70\).
Calculate \(\frac{DE}{GH}=\frac{18}{45}=\frac{2}{5}\), \(\frac{EF}{HI}=\frac{24}{60}=\frac{2}{5}\), \(\frac{FD}{IG}=\frac{28}{70}=\frac{2}{5}\)

Step2: Check the similarity criterion

Since \(\frac{DE}{GH}=\frac{EF}{HI}=\frac{FD}{IG}=\frac{2}{5}\), by the Side - Side - Side (SSS) similarity criterion, \(\triangle DEF\sim\triangle GHI\)

Answer:

\(\triangle DEF\) and \(\triangle GHI\) are similar. By the SSS (Side - Side - Side) similarity criterion, since \(\frac{DE}{GH}=\frac{EF}{HI}=\frac{FD}{IG}=\frac{2}{5}\)