Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. △abc is an isosceles triangle with (overline{ab}=overline{bc}=6) units. d and e are the midpoints of (overline{ab}) and (overline{bc}), respectively. the length of (overline{ac}) is 8 units. the length of (overline{de}) is units. reset next

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

Step2: Identify the mid - segment and the third side

In \(\triangle ABC\), \(D\) is the midpoint of \(AB\) and \(E\) is the midpoint of \(BC\). So, \(DE\) is the mid - segment and \(AC\) is the third side.

Step3: Calculate the length of \(DE\)

Given \(AC = 8\) units. By the mid - segment theorem, \(DE=\frac{1}{2}AC\).
Substitute \(AC = 8\) into the formula: \(DE=\frac{1}{2}\times8\).
\(DE = 4\)

Answer:

\(4\)