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