PQRS is a parallelogram in which PA=1/4PQ,SB=1/4SR,QD=1/4QR,PC=1/4PS if AB and CDintersect at X, show that PAXC is a parallelogram - Maths - Quadrilaterals

Question

PQRS is a parallelogram in
which PA=1/4PQ ,
SB=1/4SR ,
QD=1/4QR ,
PC=1/4PS if
AB and
CD intersect at
X, show that
PAXC is a parallelogram

Utsav · Accepted Answer

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PQRS is a parallelogram â€‹
Since PQRS ia ∥gm∴PQ∥SR and PQ=SR Also PS=QR and
PS∥QRNow PQ∥SR and PQ=SRIt means PA∥SB∥CX
and PA=SB=CX(∵PQ=SR⇒14PQ=14SR⇒PA=SB)Also PS=QR and
PS∥QRIt means PC∥QD∥AX and
PC=QD=AX(∵PS=QR⇒14PS=14QR ⇒PC=QD)Hence in a
quadrilateral when pair of opposite sides are parallel and
equal,then that quadrilateral is a parallelogram∴PAXC is a
parallelogram

PQRS is a parallelogram in which PA=1/4PQ , SB=1/4SR , QD=1/4QR , PC=1/4PS if AB and CD intersect at X, show that PAXC is a parallelogram