Question

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

Which statement is needed to prove that segment DE is half the length of segment BC?
A. Segment AD is 3, and segment AE is 4.
B. Segment AD is 3, and segment AE is 6.
C. Segment AD is 4, and segment AE is 6.
D. Segment AD is 4, and segment AE is 3.

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=(1)/(2)* AB=(1)/(2)*8=4,\\\\\\AE=(1)/(2)* AC=(1)/(2)* 6=3.`

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

Option (D) is CORRECT.