Question

if \\( \triangle hli \sim \triangle jlk \\) by the sss similarity theorem, then \\( \frac { h l } { j l } = \frac { i l } { k l } \\) is also equal to which ratio?
\\( \frac { h i } { j k } \\)
\\( \frac { h j } { j l } \\)
\\( \frac { i k } { k l } \\)
\\( \frac { j k } { h i } \\)

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:

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