Question

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

Explanation:

Step1: Calculate the ratios of corresponding sides

For sides \(DE = 9\) and \(GH=13.5\), the ratio is \(\frac{DE}{GH}=\frac{9}{13.5}=\frac{90}{135}=\frac{2}{3}\).
For sides \(EF = 7\) and \(HI = 10.5\), the ratio is \(\frac{EF}{HI}=\frac{7}{10.5}=\frac{70}{105}=\frac{2}{3}\).
For sides \(DF = 12\) and \(GI=18\), the ratio is \(\frac{DF}{GI}=\frac{12}{18}=\frac{2}{3}\).

Step2: Check similarity property

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