In triangle ABC, AD is the median and DE || AB. Prove that BE is another median. Please help! :O Sorry, i couldn't post the figure.
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6
to proof;-BE is another median
proof;-d is the midpoint of bc (as ad is median)
d is the midpoint of bc and de is parallel to ab
⇒by converse of midpoint theorem e is the midpoint of ac
∴be is another median
proof;-d is the midpoint of bc (as ad is median)
d is the midpoint of bc and de is parallel to ab
⇒by converse of midpoint theorem e is the midpoint of ac
∴be is another median
Answered by
10
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.
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.
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