Question

given trapezoid wxyz, what is xy? (simplify your answer.) xy = □□ △

Explanation:

Step1: Recall mid - segment theorem

In a trapezoid, the length of the mid - segment (the line segment connecting the mid - points of the non - parallel sides) is given by the formula \(DE=\frac{WZ + XY}{2}\), where \(DE\) is the mid - segment, \(WZ\) and \(XY\) are the lengths of the bases. Here \(DE = 28\) and \(WZ=52\).

Step2: Substitute values into formula

We have \(28=\frac{52 + XY}{2}\).

Step3: Solve for \(XY\)

Multiply both sides of the equation by 2: \(28\times2=52 + XY\), so \(56 = 52+XY\). Then subtract 52 from both sides: \(XY=56 - 52\).

Answer:

\(4\)