Question

1. de is a midsegment of △abc. find the value of x.
2. find pq.
3. find wu.
4. complete the statement. (overline{np}parallel____)

Explanation:

Step1: Recall mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. In $\triangle ABC$, since $DE$ is a mid - segment, $AE = EC$. Given $AE = 6$, then $x=6$.

Step2: For $\triangle LMN$

$PQ$ is a mid - segment. The mid - segment of a triangle is half the length of the side it is parallel to. If the side parallel to $PQ$ has length $16$, then $PQ=\frac{16}{2}=8$.

Step3: For $\triangle VWU$

$ML$ is a mid - segment. If $ML = 9$, then the side parallel to it ($WU$) has length $WU = 2\times9=18$.

Step4: In $\triangle RQS$

$MN$ is a mid - segment. By the mid - segment theorem, $\overline{NP}\parallel\overline{RQ}$.

Answer:

1. $x = 6$
2. $PQ = 8$
3. $WU = 18$
4. $\overline{NP}\parallel\overline{RQ}$