Question

question 2 (multiple choice worth 1 points) (02 05r mc) in triangle abc shown below, side ab is 10 and side ac is 8: which statement is needed to prove that segment de is parallel to segment bc and half its length? segment ad is 5, and segment ae is 4. segment ad is 4, and segment ae is 8. segment ad is 4, and segment ae is 5. segment ad is 5, and segment ae is 2.

Explanation:

Step1: Recall triangle - mid - segment theorem

The mid - segment theorem states that if a line segment joins the mid - points of two sides of a triangle, then it is parallel to the third side and half its length. In \(\triangle ABC\), for \(DE\) to be parallel to \(BC\) and half its length, \(D\) must be the mid - point of \(AB\) and \(E\) must be the mid - point of \(AC\).

Step2: Calculate mid - points

Given \(AB = 10\) and \(AC=8\). The mid - point of \(AB\) divides \(AB\) into two equal parts. So \(AD=\frac{AB}{2}=\frac{10}{2} = 5\). The mid - point of \(AC\) divides \(AC\) into two equal parts. So \(AE=\frac{AC}{2}=\frac{8}{2}=4\).

Answer:

A. Segment AD is 5, and segment AE is 4.