Question

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 - midsegment theorem

The mid - segment theorem states that if a line segment joins the mid - points of two sides of a triangle, then the line segment is parallel to the third side and half its length.

Step2: Find mid - points of AB and AC

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

Answer:

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