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Question

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
1060326_ed3f6178953046e29c83715ceb3c82e5.png

Solution
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ABCD is a parallelogram

AB||CD

AE||CF & AB=CD

12AB=12CDAE=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

ΔDQC ΔABP
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=DP PQ=QB

PQ=DP=BQ

Hence the line segment AE & EC triset the diagonal BD.

1205264_1060326_ans_ff8ed2a7ebde42a3a536f3f442e0cb2d.png

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