Question

triangle xyz is formed by connecting the midpoints of the side of triangle uvw. the lengths of the sides of triangle uvw what is the length of \\(\overline{xy}\\)? figures not necessarily drawn to scale.
image of triangle uvw with midpoints x, y, z forming triangle xyz, side lengths marked: wv=6, wu=6, uv=8
answer attempt 1 out of 2
\\(xy = \square\\) submit answer

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 side

In triangle \(UVW\), segment \(XY\) is a mid - segment. The side parallel to \(XY\) is \(UW\).

Step3: Calculate the length of \(XY\)

Since \(XY=\frac{1}{2}UW\) and \(UW = 6\), then \(XY=\frac{6}{2}=3\)

Answer:

\(3\)