Question

complete the sentence if \\(\overline{de}\\) is the midsegment opposite \\(\overline{ac}\\) in \\(\triangle abc\\), then \\(\overline{de}\parallel\overline{ac}\\) and \\(de = \square ac\\) by the triangle midsegment theorem.

Explanation:

Step1: Recall the Triangle Midsegment Theorem

The Triangle Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

Step2: Apply the theorem to the given problem

In $\triangle ABC$, $\overline{DE}$ is the midsegment opposite $\overline{AC}$. By the Triangle Midsegment Theorem, $DE$ is parallel to $AC$ and $DE = \frac{1}{2}AC$.

Answer:

$\frac{1}{2}$