Question

can the triangles be proven similar using the sss or sas similarity theorems?
yes, △efg - △klm only by sss.
yes, △efg - △klm only by sas
yes, △efg ~ △klm by sss or sas
no, they cannot be proven similar by sss or sas

Explanation:

Step1: Check SAS similarity

Compare sides around equal angles. For $\triangle EFG$ and $\triangle KLM$, the included angles are equal. Calculate ratios: $\frac{EF}{LM}=\frac{18}{5}$, $\frac{FG}{KL}=\frac{15}{6}=\frac{5}{2}$, $\frac{EG}{KM}=\frac{24}{8}=3$. The ratios of sides around the equal angle are not equal ($\frac{18}{5}
eq \frac{15}{6}$).

Step2: Check SSS similarity

Check if all corresponding sides have equal ratios: $\frac{EF}{LM}=\frac{18}{5}=3.6$, $\frac{FG}{KL}=\frac{15}{6}=2.5$, $\frac{EG}{KM}=\frac{24}{8}=3$. Ratios are not equal.

Answer:

No, they cannot be proven similar by SSS or SAS