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 { hi } { 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:

A. \(\frac{HI}{JK}\)