Question

triangle uvw is formed by connecting the midpoints of the side of triangle rst. the lengths of the sides of triangle rst are shown. what is the length of \\( \overline { u v } \\)? 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.

Step2: Identify the relevant side

In \(\triangle RST\), \(UV\) is a mid - segment. \(UV\) is parallel to \(TR\) and \(UV=\frac{1}{2}TR\).

Step3: Calculate the length of \(UV\)

Given \(TR = 10\), then \(UV=\frac{1}{2}\times10 = 5\).

Answer:

$5$