Question

triangle ghi is formed by connecting the midpoints of the side of triangle def. the lengths of the sides of triangle ghi are shown. what is the length of (overline{ef})? figures not necessarily drawn to scale.

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. In \(\triangle DEF\), \(\triangle GHI\) is formed by connecting mid - points. So, each side of \(\triangle GHI\) is a mid - segment of \(\triangle DEF\).

Step2: Identify the mid - segment related to \(EF\)

The side \(HI\) of \(\triangle GHI\) is the mid - segment parallel to \(EF\). According to the mid - segment theorem, if \(HI\) is a mid - segment, then \(EF = 2\times HI\).

Step3: Substitute the value of \(HI\)

From the figure, \(HI = 4\). So, \(EF=2\times4\).

Answer:

\(8\)