Question

if ( \triangle hli sim \triangle jlk ) by the sss similarity theorem, then ( \frac{hl}{jl}=\frac{il}{kl} ) is also equal to which ratio? ( \frac{hi}{jk} ) ( \frac{hj}{jl} ) ( \frac{ik}{kl} ) ( \frac{jk}{hi} )

Explanation:

Step1: Recall SSS similarity theorem

If \(\triangle HLI\sim\triangle JLK\) by SSS (Side - Side - Side) similarity theorem, then the ratios of corresponding sides are equal.

Step2: Identify corresponding sides

In similar triangles \(\triangle HLI\) and \(\triangle JLK\), \(HL\) corresponds to \(JL\), \(IL\) corresponds to \(KL\), and \(HI\) corresponds to \(JK\).
So, \(\frac{HL}{JL}=\frac{IL}{KL}=\frac{HI}{JK}\)

Answer:

\(\frac{HI}{JK}\) (i.e., the first option)