Question

$\overline{\mathit{M}\mathit{N}}$is the median of trapezoid $ZOID$.

If localid="1638355391309" $ZO=8$and $MN=11$, then $DI=\underset{¯}{}$.

Short answer

If $ZO=8$and $MN=11$, then $DI=14$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

The theorem 5-19 states that the median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.

It is being given that $\overline{MN}$is the median of trapezoid $ZOID$.

From the given diagram it can be noticed the sides ZO and DI are parallel sides, therefore the bases of the trapezoid ZOID are ZO and DI.

Therefore, by using the theorem 5-19 it can be noticed that the median $\overline{MN}$is parallel to the bases ZO and DI and has a length equal to the average of the base lengths ZO and DI.

Therefore, $MN=\frac{1}{2}\left(ZO+DI\right)$.

Therefore, it can be obtained that:

$\begin{array}{c}MN=\frac{1}{2}\left(ZO+DI\right)\\ 11=\frac{1}{2}\left(8+DI\right)\\ 22=8+DI\\ 22-8=DI\\ 14=DI\end{array}$

Therefore the length of DI is 14.

Step 3. Write the complete statement.

If $ZO=8$and $MN=11$, then $DI=14$.