In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD
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ABCD is a parallelogram
∵AB||CD
⇒AE||CF & AB=CD
12AB=12CD⇒AE=OF
in AECF
AE||CF adn AE=CF
One pair of opposite sides is equal to 11
AECF is a parallelogram
∵AF||CF
⇒PF||CQ and AP||EQ
ΔDQCΔABP
F is the mid point of DC & PF||CQ E is the mid point of AB and AP||EQ
P is the mid point od DQ Q is the mid point of BP
⇒PQ=DPPQ=QB
PQ=DP=BQ
Hence the line segment AE & EC triset the diagonal BD.
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