Question

guided practice
midsegments of triangles
type your answer and then click or tap done.
what is the length of \\( \overline { x y } \\) ?

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem of a triangle states that the length of the mid - segment (a segment connecting the mid - points of two sides of a triangle) is half the length of the third side.

Step2: Identify the mid - segment and the third side

In triangle \(VWU\), \(XY\) is the mid - segment (since \(X\) is the mid - point of \(VU\) and \(Y\) is the mid - point of \(WU\)), and \(VW = 26\) is the side parallel to \(XY\).
According to the mid - segment theorem \(XY=\frac{1}{2}VW\).

Step3: Calculate the length of \(XY\)

Substitute \(VW = 26\) into the formula \(XY=\frac{1}{2}VW\). So \(XY=\frac{1}{2}\times26 = 13\).

Answer:

\(13\)