Question

In the following figure, a trapezoid$ABCD$has median$\overline{MN}$. If $FC=9$then find.EN

Short answer

The measure of$EN=4.5$units.

Step-by-step solution

Step 1- Apply the concept of mid segment theorem.

The trapezoid midsegment theorem states that the length of the midsegment is equal to the sum of the base lengths divided by 2.

Also, the segment that joins the midpoints of two sides of a triangle is half as long as the third side.

Step 2- Check the figure.

Consider the figure.

Step 3- Step description.

Here$\overline{EN}$ is the median of$\Delta BFC$ and$FC=9$ .

Use the mid segment theorem and find the value of$EN$ as follows:

$\begin{array}{l}\overline{EN}=\frac{1}{2}\overline{FC}\\ \overline{EN}=\frac{1}{2}\left(9\right)\\ \overline{EN}=4.5\end{array}$

Therefore, the measure of$\overline{EN}=4.5$ units.