Question

In Triangle ABC shown below, side AB is 6 and side AC is 4.

Answer 1

Answer: A is the correct option.Segment AD is 3 and segment AE is 2.

Step-by-step explanation:

Given : A triangle ABC  where AC=4 and AB=6

then to prove segment DE is parallel to segment BC and half its length.

the length of AD and AE must divide AC and AB respectively to get the same ratio of 2:1

To apply converse of basic proportionality theorem.

If we take first option Segment AD is 3 and segment AE is 2 then

$\frac{AB}{AD}=\frac{6}{3}=\frac{2}{1},\frac{AC}{AE}=\frac{4}{2}=\frac{2}{1}\\\Rightarrow\frac{AB}{AD}=\frac{AC}{AE}$

Therefore by converse of basic proportionality theorem

DE is parallel to segment BC and half its length.

Therefore A is correct option.

Answer 2

The correct answer to this question is "Segment AD is 3 and segment AE is 2." Since we need a half length side, then they should be proportion. We prove that segment DE is parallel to segment BC and half its length by dividing the length of AB and AC. Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help.