Question

determine if \\( \triangle efg \\) is similar to \\( \triangle rts \\).

no, the triangles are not similar.
there is not enough information to prove these triangles are similar.
yes, the triangles are similar.

Explanation:

Step1: Calculate the ratios of corresponding sides

For \(\triangle EFG\) and \(\triangle RTS\), check the ratios of the sides.
\(\frac{EF}{RS}=\frac{3}{21}=\frac{1}{7}\), \(\frac{EG}{RT}=\frac{7}{9}\), \(\frac{FG}{TS}=\frac{5}{15}=\frac{1}{3}\)

Step2: Check similarity condition

Since \(\frac{EF}{RS}
eq\frac{EG}{RT}
eq\frac{FG}{TS}\), the sides are not in proportion.

Answer:

No, the triangles are not similar.