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.
(images of triangles: △efg with sides 18, 24, 15 and △klm with sides 6, 8, 5, and marked angles at f and l)

Explanation:

Step1: List sides of both triangles

△EFG: EF=18, FG=15, EG=24; △KLM: KL=6, LM=5, KM=8

Step2: Check SSS similarity

Ratios: $\frac{EF}{KL}=\frac{18}{6}=3$, $\frac{FG}{LM}=\frac{15}{5}=3$, $\frac{EG}{KM}=\frac{24}{8}=3$. All equal.

Step3: Check SAS similarity

Included angles (marked) are equal. Ratios of adjacent sides: $\frac{EF}{KL}=\frac{FG}{LM}=3$. SAS holds.

Step4: Evaluate options

Both SSS and SAS apply.

Answer:

Yes, △EFG ~ △KLM by SSS or SAS.