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Question
In triangle ABC, angle B is obtuse. D and E are mid-points of sides AB and BC respectively and F is a point on side AC such that EF is parallel to AB. Show that BEFD is a parallelogram.
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Solution
The figure is shown below
AD = DB
BE = EC
EF || BD
In Δ ABC
E is the midpoint of AB and
EF || BD
∴ By the midpoint theorem, F will be the midpoint of AC and D will be the midpoint of AB.
As D and F are midpoints of AC and AB respectively.
∴ By the midpoint theorem of DF || BC or BE
Since DF || BE and EF || BD
Hence, BEFD is a parallelogram.
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