Q. 53.6( 39 Votes )

In figure 5.25, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that 􀀍PQRS is a parallelogram.


Answer :

Given ABCD is a parallelogram so

AD = BC and AD BC


and DC = AB and DC AB


also AP = BQ = CR = DS


AS = CQ and PB = DR


in ΔAPS and Δ CRQ


A = C (opposite s of a parallelogram are congruent)


AS = CQ


AP = CR


ΔAPS Δ CRQ( SAS congruence rule)


PS = RQ (c.p.c.t.)


Similarly PQ= SR


Since both the pair of opposite sides are equal


PQRS is gram.


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