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Question

State true or false:

In the given figure, diagonals PR and QS of the parallelogram PQRS intersect at point O and LM is parallel to PS, that
Area (ΔPOS)+ Area (ΔQOR)= Area (ΔPOQ)+ Area (ΔSOR)

187522_54135e4e0dac4cc7917fc7ea130fbfb0.png

A
True
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B
False
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Solution

The correct option is A True
In (ΔPOS) and (ΔSOR)
PO=OR (diagonal bisects eachother)
POS=SOR (900)
OS=OS (common side)
POS(ΔSOR) (SAS congrience)
Area of POS = Area SOR
In (ΔQOR) and (ΔPOQ)
OP=OR (diagonal bisects eachother)
POQ=QOR (900)
OQ=OQ (common side)
QOS(ΔQOR) (SAS congrience)
Area of QOS = Area QOR
Area of parallelogram PQRS=Area of POS+Area of POQ+Area of QOR+Area of SOR
=Area of SOR+Area of SOR+Area of POQ+Area of POQ
=2SOR+2AreaofPOQ
2POS+2QOR=2SOR+2POQ
Area(POS)+Area(QOR)=Area(POQ)+Area(SOR)

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