Question

In a triangle $ABC$, $D$ is the midpoint of $AB$ and $E$ is a point on $AC$ such that $DE||BC$. Then

• A. AE=EC
• B. AE= AC/2
• C. Both of the above
• D. Neither of the above

Answer 1

The correct option is C

Both of the above

Converse of mid-point theorem: It states that in a triangle line drawn from the mid-point of the one side of triangle, parallel to the other side intersect the third side at its mid-point.
With the given conditions, we can say by using the converse of the midpoint theorem that E will be the midpoint of AC. Looking at the options, we see that both the first and second options satisfy the condition that E is the midpoint of AC. Thus, the right option is option 3.