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Question
In triangle ABC ; D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F.
Prove that BDEF is a parallelogram. If AB = 16 cm, AC = 12 cm and BC = 18 cm,
find the perimeter of the parallelogram BDEF.
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Solution
The figure is shown below
From figure since E is the midpoint of AC and EF || AB
Therefore F is the midpoint of BC and 2DE = BC or DE = BF
Again D and E are midpoints,
therefore DE || BF and EF = BD
Hence BDEF is a parallelogram.
Now,
BD = EF = `1/2"AB" = 1/2` x 16 = 8 cm
BF = DE = `1/2"BC" = 1/2` x 18 = 9 cm
Therefore perimeter of BDEF = 2( BF + EF ) = 2( 9 + 8 ) = 34 cm.
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