Question

1. what similarity property, if any, can be used to show that the following two triangles are similar. sss not enough information given aa sas

Explanation:

Step1: Check side - length ratios

For $\triangle DEF$ with side - lengths $DE = 8$, $EF=6$, $DF = 10$ and $\triangle GHI$ with side - lengths $GH = 12$, $HI = 9$, $GI=15$. Calculate the ratios of corresponding sides: $\frac{DE}{GH}=\frac{8}{12}=\frac{2}{3}$, $\frac{EF}{HI}=\frac{6}{9}=\frac{2}{3}$, $\frac{DF}{GI}=\frac{10}{15}=\frac{2}{3}$.

Step2: Apply similarity criterion

Since the ratios of all three pairs of corresponding sides of $\triangle DEF$ and $\triangle GHI$ are equal, by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

A. SSS