Question

triangle qrs is formed by connecting the midpoints of the side of triangle nop. the lengths of the sides of triangle nop are shown. what is the length of qs? 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 \(\triangle NOP\), \(QS\) is a mid - segment.

Step2: Identify the side it is parallel to

\(QS\) is parallel to \(OP\).

Step3: Apply the mid - segment formula

Since \(QS=\frac{1}{2}OP\) and \(OP = 6\), then \(QS=\frac{1}{2}\times6\).

Answer:

\(3\)