In a parallelogram ABCD, E and F are mid points of sides AB and CD. Show that line segment AF and CE trisect the diagonal BD.
ABCD is a parallelogram.
AB || CD
And hence, AE || FC
Again, AB = CD (Opposite sides of parallelogram ABCD)
AE = FC (E and F are mid-points of side AB and CD)
In quadrilateral AECF, one pair of opposite sides (AE and CF) is parallel and equal to each other.
Therefore, AECF is a parallelogram.
DF = CF (given)
DP = PQ ....(i) (by converse of mid-point them)
AE = BE (given)
AP || EQ
PQ = QB ….(ii) (by converse of mid-point them)So, DP = PQ = QB
Hence, line segment AF and CE trisect the diagonal BD.
You have rated this answer /10