ABCD is a parallelogram and E is the
midpoint of BC . The side DC
is extended such that it meets AE, when
extended, at F. Prove that DF = 2DC
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ABCD is a parallelogram and E is the midpoint of BC, such that if AB and it is extended they meet at point F.
In ΔBAE and ΔEFC
Since, AD // BC (sides of parallelogram)
DAB and EBF are interior alternate angles.
Vertically opposite angles.
Since, E is the midpoint, it divides BC into equal parts.
by AAS property.
So, by C. P. C. T. C
Now,
Since,
CF = AB (As proved above)
AB = DC (Opposite sides of parallelogram)
So,
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