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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.

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

ABCD is a parallelogram.

AB || CD

And hence, AE || FC

Again, AB = CD (Opposite sides of parallelogram ABCD)

AB =CD

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.

In DCQ,

DF = CF (given)

PF||QC

DP = PQ ....(i) (by converse of mid-point them)

In ABP,

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.

Answered by Expert 4th June 2014, 3:23 PM
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