Question

quadrilateral mnop below is a trapezoid. use the figure to select the best answer from the choices provided. if hg = 14, what is the sum of po and mn? select the best answer from the choices provided. a. 3.5 b. 14 c. 17 d. 28

Explanation:

Step1: Recall the trapezoid mid - segment theorem

The length of the mid - segment of a trapezoid \(HG=\frac{PO + MN}{2}\), where \(HG\) is the mid - segment of trapezoid \(MNOP\) (since \(H\) is the mid - point of \(PM\) and \(G\) is the mid - point of \(ON\)).

Step2: Solve for \(PO + MN\)

Given \(HG = 14\), from the formula \(HG=\frac{PO + MN}{2}\), we can multiply both sides of the equation by \(2\). So \(PO + MN=2\times HG\).
Substitute \(HG = 14\) into the equation: \(PO + MN=2\times14\).

Answer:

\(D. 28\)