Question

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that DP=1/3DB

Answer 1

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Answer 2

Given : In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively.

To Find :  Show that DP=1/3DB

Solution:

ABCD is parallelogram

AB || CD  & AB = CD

E & F are mid point of AB  & CD

=> AE = CF

AE || CF  as E & F are points on AB & CD

=> AECF is a parallelogram

=> AF || EC

in ΔDQC

PF || QC   ∵ AF || EC

As F is mid point of DC

Hence P is mid point of DQ

=> DP = PQ

Similarly

BQ =  PQ

=> BQ = DP

DB = BQ + PQ + DP

=> BD = DP + DP + DP

=> BD = 3DP

=> DP = BD/3

=> DP = DB/3

QED

Hence proved

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