Question

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

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

Step2: Identify the relevant sides

In \(\triangle GHI\), segment \(\overline{JK}\) is a mid - segment. The side parallel to \(\overline{JK}\) is \(\overline{GI}\) and \(GI = 6\).

Step3: Calculate the length of \(\overline{JK}\)

By the mid - segment theorem, \(JK=\frac{1}{2}GI\). Substitute \(GI = 6\) into the formula: \(JK=\frac{1}{2}\times6 = 3\).

Answer:

$3$