Question

# In the given figure, diagonals PR and QS of the parallelogram PQRS intersect at point O and LM is parallel to PS. Show that : Area (Δ POS) + Area (Δ QOR) = Area (Δ POQ) + Area (Δ SOR).

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Solution

## In given figure parallelogram PQRS , PR and QS diagonal intersect at O.We know that the diagonal intersect at right angle each other The line LM is parallel to PS Then diagonal of parallelogram divided in equal area of triangles Then area Δ POQ= area of Δ POS=area of ΔQOR=area of Δ SOROR Area of Δ POS +area of Δ QOR=12 = area of parallelogram Then area of Δ POS +area of ΔQOR=area of ΔPOQ +area ΔSOR

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