Question

which property of similarity can be used to prove triangles def and ghi are similar?
not enough information
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sas
sss

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangles \(DEF\) and \(GHI\), we have:

• \(\frac{DE}{GH}=\frac{9}{13.5}=\frac{90}{135}=\frac{2}{3}\)
• \(\frac{EF}{HI}=\frac{7}{10.5}=\frac{70}{105}=\frac{2}{3}\)
• \(\frac{DF}{GI}=\frac{12}{18}=\frac{2}{3}\)

Step2: Apply the SSS similarity criterion

Since \(\frac{DE}{GH}=\frac{EF}{HI}=\frac{DF}{GI}=\frac{2}{3}\), by the SSS (Side - Side - Side) similarity criterion, triangles \(DEF\) and \(GHI\) are similar.

Answer:

SSS