Maths / Areas Of Parallelograms And Triangles / Median and Altitude of Triangle

QUESTION
 

In the given figure, O is any point on diagonal PR of parallelogram PQRS. Prove that large ar(POS)=ar(PQO).

EXPLANATION
Explain TypeExplanation Content
Text

Given : PQRS is a parallelogram.

Proof : SQ is a diagonal.

M is the midoint of SQ.

therefore              OM is a median of Delta SOQ

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ar(SMO)=ar(QMO)                       (Median divides the triangle in 2 equal areas)  .............. (1)

Also,

In  Delta SQR,;RM is median.

therefore : : : : : : : : : : : ar(SMR)=ar(QMR): : : : : : : : : : ..........(2)

Subtracting (1) and (2), we get

Rightarrow : : : : : : ar(SOR)=ar(QOR)

Now, PR is a diagonal.

therefore : : : : : : : : : : : ar(Delta PSR)=ar(Delta PQR)             (Diagonal divides the parallelogram in 2 equal areas)

Rightarrow : : : : : ar(PSO)+ar(SOR)=ar(POQ)+ar(OQR)

Rightarrow : : : : : ar(PSO)=ar(POQ)

Hence proved

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