Question

determine if triangle ( abc ) and triangle ( def ) are or are not similar, and, if they are, state how you knc (note that figures are not necessarily drawn to scale.) answer attempt 1 out of 2 the triangles are similar because

Explanation:

Step1: Calculate the ratios of corresponding sides

For side \(AC = 26\) and \(DF=52\), the ratio is \(\frac{AC}{DF}=\frac{26}{52}=\frac{1}{2}\).
For side \(BC = 28\) and \(EF = 56\), the ratio is \(\frac{BC}{EF}=\frac{28}{56}=\frac{1}{2}\).
For side \(AB=19\) and \(DE = 38\), the ratio is \(\frac{AB}{DE}=\frac{19}{38}=\frac{1}{2}\).

Step2: Check the similarity criterion

Since \(\frac{AC}{DF}=\frac{BC}{EF}=\frac{AB}{DE}=\frac{1}{2}\), by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

The triangles are similar because the ratios of their corresponding sides are equal (\(\frac{AC}{DF}=\frac{BC}{EF}=\frac{AB}{DE}=\frac{1}{2}\)), satisfying the SSS (Side - Side - Side) similarity criterion.