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Question
In triangle ABC,AD is the median and DE, drawn parallel to side BA, meets AC at point E. Show 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 is drawn from the mid point of BC i.e.D, then by 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.
Hope you understand it.
Since AD is the median of ΔABC, then BD = DC.
Given,DE || AB and DE is drawn from the mid point of BC i.e.D, then by 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.
Hope you understand it.
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