A parallelogram ABCD has E as the midpoint of DC and F a point on AC such that CF = (1/4) AC, EF produced meets BC at G. Prove that G is the mid-point of BC.
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mishraraghavraman:
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Answer:
E is the midpoint of AC
therefore
EC = 1/2 AC
D is the midpoint of BC
And BE || DF
therefore
F is the midpoint of EC
[converse midpoint theorem]
CF = 1/2 x EC
= 1/2 x (1/2 x AC )
=1/4 x AC
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