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Triangle Inequality

In a triangle...

Question

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

AE=EC

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AE= AC/2

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Both of the above

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Neither of the above

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Solution

The correct options are
A
AE=EC

B
AE= AC/2

With the given conditions, we can say by using the inverse 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.
AE=EC
also AE = $\frac{1}{2} A C$
rest conditionare not true.

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