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Question
In Δ ABC, AD is the median and DE is parallel to BA, where E is a point in AC. Prove that BE is also a median.
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Solution
Since AD is the median of ΔABC, then BD = DC.
Given, DE || AB and DE are drawn from the midpoint of BC i.e. D, then
by the converse of mid-point theorem,
it bisects the third side which in this case is AC at E.
Therefore, E is the mid point of AC.
Hence, BE is the median of ΔABC.
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