Question

$\overline{\mathrm{MN}}$is the median of trapezoid $\mathbf{ZOID}$.

20. If$\mathbf{ZO}\mathbf{=}\mathbf{8}$ and$\mathbf{MN}\mathbf{=}\mathbf{11}$ , then $\mathrm{DI}=\underset{\_}{?}$.

Short answer

If$ZO=8$ and$MN=11$ , then$\mathbf{DI}\mathbf{=}\mathbf{14}$ .

Step-by-step solution

­- Observe the given diagram.

The given diagram is:

- 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 are and .

Therefore, by using the theorem 5-19 it can be noticed that the median is parallel to the basesand and has a length equal to the average of the base lengths and .

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

Therefore, it can be obtained that:

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

Therefore the length D of is 14.

- Write the complete statement.

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