Question

In fig, X and Y are respectively the mid points of the opposite sides AD and BC of a parallelogram ABCD. Also, BX and DY intersect AC at P and Q, respectively. Show that AP=PQ=QC.

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Answer 1

Using Mid Point Theorem

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Answer 2

Answer:

From the figure,

AB = BC .....(opposite sides of a parallelogram )

Therefore, DX = BY ...(1 2 AD = 1 2 BC)

Also, DX || BY ...(As AD || BC)

So, XBYD is a parallelogram.

(A pair of opposite sides equal and parallel)

i.e., PX || QD

Therefore, AP = PQ ...(I) ...[From ΔAQD where X is mid-point of AD]

Similarly, from ΔCPB,

CQ = PQ ...(II)

Thus, from equations (I) & (II)

AP = PQ = CQ ,,

— Hence proved.....