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 mid - point theorem

The line segment joining the mid - points of two sides of a triangle is parallel to the third side and half its length.

Step2: Identify relevant sides

In \(\triangle UVW\), \(ZY\) is the line segment joining the mid - points of two sides. Assume the side of \(\triangle UVW\) parallel to \(ZY\) has length \(4\).

Step3: Calculate length of \(ZY\)

By the mid - point theorem, if the length of the parallel side of \(\triangle UVW\) is \(l = 4\), then the length of \(ZY=\frac{1}{2}\times4\).

Answer:

2