Mathematics
In △ 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.
Mid-point Theorem
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Answer
By converse of mid-point theorem,
The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side.
In △ ABC,
Since, AD is the median.
∴ D is the mid-point of BC.
Since, D is mid-point of BC and DE || AB.
∴ E is the mid-point of AC. (By converse of mid-point theorem)
Join BE.
Hence, proved that BE is also a median.
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