Question

triangle uvw is formed by connecting the midpoints of the si e of tr ngle rst the lengths of the sides of triangle rst are shown. what is the length of vw? 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 \(RST\), \(UV\) is parallel to \(RT\), \(UW\) is parallel to \(ST\), and \(VW\) is parallel to \(RS\). Also, \(VW=\frac{1}{2}RS\).

Step2: Identify the length of \(RS\)

From the figure, the length of \(RS = 4\).

Step3: Calculate the length of \(VW\)

Using the formula \(VW=\frac{1}{2}RS\), substitute \(RS = 4\) into the formula. So \(VW=\frac{1}{2}\times4\).

Answer:

\(2\)