Question is Incomplete, Complete question is given below:
In Triangle ABC shown below, side AB is 6 and side AC is 4.
Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Answer
Segment AD is 3 and segment AE is 2.
Segment AD is 3 and segment AE is 4.
Segment AD is 12 and segment AE is 4.
Segment AD is 12 and segment AE is 8.
Answer:
Segment AD is 3 and segment AE is 2.
Step-by-step explanation:
Given:
side AB = 6
side AC = 4
Now we need to prove that segment DE is parallel to segment BC and half its length.
Solution:
Now AD + DB = AB also AE + EC = AC
DB = AB - AD also EC = AC - AE
Now we take first option Segment AD is 3 and segment AE is 2.
Substituting we get;
DB = 6-3 = 3 also EC = 4-2 =2
From above we can say that;
AD = DB and EC = AE
So we can say that segment DE bisects Segment AB and AC equally.
Hence From Midpoint theorem which states that;
"The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side."
Hence Proved.
