Question

triangle xyz is formed by connecting the midpoints of the sides of triangle uvw. the lengths of the sides of triangle uvw are shown. what is the length of zy? 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 \(UVW\), \(ZY\) is a mid - segment. The side parallel to \(ZY\) has a length of \(4\).

Step3: Apply the mid - segment theorem formula

If \(ZY\) is a mid - segment, then \(ZY=\frac{1}{2}\times\) (length of the parallel side). Since the parallel side has length \(4\), \(ZY = 2\)

Answer:

\(2\)