Answer: The correct option is
(D) Segment AD is 4, and segment AE is 3.
Step-by-step explanation: In the given figure, we are shown a triangle ABC with side AB measures 8 units and AC measures 6 units.
We are to select the statement that is needed to prove that segment DE is half the length of segment BC.
Midpoint Theorem :
The line joining the mid points of any two sides of a triangle is parallel to the third side and is half of the third side.
In triangle ABC, applying the midpoint theorem,
for DE to be half of BC, D must be the midpoint of AB and E must be the midpoint of AC.
If so, then
[tex]AD=\dfrac{1}{2}\times AB=\dfrac{1}{2}\times8=4,\\\\\\AE=\dfrac{1}{2}\times AC=\dfrac{1}{2}\times 6=3.[/tex]
Thus, for DE to be half of BC, segment AD is 4 and segment AE is 3.
Option (D) is CORRECT.
