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 SSS similarity

Calculate the ratios of corresponding sides.
For $\triangle EFG$ and $\triangle KLM$:
$\frac{EF}{KL}=\frac{18}{6} = 3$, $\frac{FG}{LM}=\frac{15}{5}=3$, $\frac{EG}{KM}=\frac{24}{8}=3$.
Since $\frac{EF}{KL}=\frac{FG}{LM}=\frac{EG}{KM} = 3$, by SSS (Side - Side - Side) similarity theorem, $\triangle EFG\sim\triangle KLM$.

Step2: Check SAS similarity

We know that the included angles (the angles between the sides) are equal (given as equal in the figure).
Also, $\frac{EF}{KL}=\frac{18}{6} = 3$ and $\frac{FG}{LM}=\frac{15}{5}=3$.
Since the ratio of two pairs of corresponding sides is equal and the included angles are equal, by SAS (Side - Angle - Side) similarity theorem, $\triangle EFG\sim\triangle KLM$.

Answer:

Yes, $\triangle EFG\sim\triangle KLM$ by SSS or SAS