Question

in \\( \triangle hij, \overline { h i } \parallel \overline { k l } \\). given that \\( j h = 18, j k = 10 \\), and \\( k l = 25 \\), find \\( h i \\).

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \( \overline{HI}\parallel\overline{KL} \), we have \( \triangle JKL\sim\triangle JHI \). By the property of similar triangles, \(\frac{JK}{JH}=\frac{KL}{HI}\).

Step2: Substitute the given values

We know that \(JH = 18\), \(JK = 10\), and \(KL = 25\). Substituting into \(\frac{JK}{JH}=\frac{KL}{HI}\), we get \(\frac{10}{18}=\frac{25}{HI}\).

Step3: Solve for \(HI\)

Cross - multiply: \(10\times HI=18\times25\). Then \(10HI = 450\). Divide both sides by 10: \(HI=\frac{450}{10}=45\).

Answer:

\(HI = 45\)