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.) answer attempt 1 out of 2 the triangles similar.

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(DEF\) with sides \(20\), \(22\), \(23\) and triangle \(GHI\) with sides \(60\), \(66\), \(69\).
The ratio of the first pair of sides: \(\frac{20}{60}=\frac{1}{3}\)
The ratio of the second pair of sides: \(\frac{22}{66}=\frac{1}{3}\)
The ratio of the third pair of sides: \(\frac{23}{69}=\frac{1}{3}\)

Step2: Check the similarity criterion

Since the ratios of all three pairs of corresponding sides are equal (\(\frac{1}{3}\)), by the Side - Side - Side (SSS) similarity criterion, the triangles are similar.

Answer:

The triangles are similar.