Question

For the following figure, given that $ABCD$is a trapezoid with median $\overline{MN}$.

If $DC=6,AB=16$then find $ME,FN,EF$.

Short answer

The values are $ME=3,FN=3,EF=5$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

Since $MN$is a median therefore

$\begin{array}{l}ME=\frac{1}{2}DC\\ ME=\frac{1}{2}\times 6\\ ME=3\\ FN=\frac{1}{2}DC\\ FN=\frac{1}{2}\times 6\\ FN=3\end{array}$

Step 3. Step description.

As from the figure, $EF=\frac{1}{2}\left(AB-DC\right)$.

Substitute the values in the formula as follows:

$\begin{array}{l}EF=\frac{1}{2}\left(AB-DC\right)\\ EF=\frac{1}{2}\left(16-6\right)\\ EF=5\end{array}$

Therefore, the values are $ME=3,FN=3,EF=5$.