Question

In triangle ABC shown below, side AB is 8 and side AC is 6:

Answer 1

The answer is C because AD is half of AB and AE is half of AC.

Answer 2

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

$AD=\dfrac{1}{2}\times AB=\dfrac{1}{2}\times8=4,\\\\\\AE=\dfrac{1}{2}\times AC=\dfrac{1}{2}\times 6=3.$

Thus, for DE to be half of BC, segment AD is 4 and segment AE is 3.

Option (D) is CORRECT.