Question

determining whether triangles are similar
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 and klm with side lengths: efg has sides 24, 15, 18; klm has sides 8, 6, 5, and marked angles at f and l)

Explanation:

Step1: Identify corresponding sides

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

Step2: Check side ratios

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

Step3: Check SAS condition

No included angle measure given for both triangles, so SAS can't be applied.

Answer:

Yes, △EFG ~ △KLM only by SSS.